detection of flow pulsation by micro-controller equipped

MASTER’S THESIS

2006:39 PB

Shuvra Dev Sarker

Detection of Flow Pulsation byMicro-controller Equipped

Ultrasonic Flow Meter

Department of Computer Science and Electrical EngineeringEISLAB • Embedded Internet Systems Laboratory

M.Sc. in Computer Sciences and EngineeringCONTINUATION COURSES

2006:39 PB • ISSN: 1653 - 0187 • ISRN: LTU - PB - EX - - 06/39 - - SE

Detection of Flow Pulsation byMicro-controller Equipped Ultrasonic

Flow Meter

Shuvra Dev Sarker

Lulea University of TechnologyDept. of Computer Science and Electrical Engineering

EISLAB

August 2006

Supervisor: Jan van DeventerLuleå University of Technology

ABSTRACT

This thesis demonstrates that the small micro-controller present in ultrasonic flow meters

can detect error inducing flow pulsations. The implemented code is provided in the

appendices.

The application targets the district heating industry where the use of ultrasonic flow

meters is growing more and more common as they are accurate, non-intrusive and low

cost. District heating companies desire accurate and low cost flow measurement. An

underestimation of the flow rate leads to a loss of income and the total cost of measuring,

the reading, maintenance and installation represents a relatively large part of the total

cost.

Recently, in competitive market, micro-controllers have become inexpensive and those

are capable of doing complex computations. In this thesis, as part of self-diagnosis tech-

niques, the detection of the pulsating flow is implemented on an 8-bit ATMEL AVR

micro-controller. It saves a huge installation cost and is economically beneficial for an

industry. Serial communication and data conversion are also implemented to receive ve-

locity input data. The work shows that even with an 8-bit micro-controller flow pulsations

are detectable.

Keywords: FFT, DFT, Pulsating flow, Ultrasonic Flow Meter, Hamming window, At-

mel AVR.

iii

PREFACE

The research described in this Master’s thesis was carried out during spring 2006 at Lulea

University of Technology, under the division of EISLAB.

First and foremost, I would like to thank and express my gratitude to my Supervisor

Dr. Jan van Deventer, Head of the EISLAB, Lulea University of Technology, Sweden, for

his supervision and immense contributions in shaping this thesis. His inspiration helps

me to finish this thesis.

I would like to express my gratitude to Johan Eriksson and David Johansson for their

interesting discussions about Atmel AVR and Signal System.

A special thank also goes to David A. Carr, who has always helped me to provide

valuable feedback related to educational and administrative purposes that make possible

to complete my Master degree.

I would like to express my gratitude to Shahidul Islam Sheikh who has helped and

guided me in countless ways every day of my life in Sweden. I would like to express

my gratitude to Mr. Atanu Nath, PhD student at Division of Industrial Marketing and

e-Commerce, Lulea University of Technology, who has always guided me in numerous

ways despite having his own research workload.

My thanks go also to Sweden, and the people of Sweden, for the warm embrace, it has

given me these past years. I feel honored to have known you.

Finally, I want to express my gratitude to my parents and my brother to whom I

dedicate this thesis for their constant support. It is my greatest blessings to be their son.

v

To my loving parents,

Nirapada Sarker and Monimala Sarker

vi

CONTENTS

Chapter 1: Introduction 3

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 2: Background 5

2.1 Flow meters summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Transit-Time Ultrasonic Flow Meters . . . . . . . . . . . . . . . . . . . . 7

2.3 Problems of Ultrasonic Flow Meters . . . . . . . . . . . . . . . . . . . . . 9

2.4 Carlander’s Self Diagnostics for Ultrasonic Flow Measurement . . . . . . 10

2.5 Berrebi’s Detection of Pulsating Flows in an Ultrasonic Flow Meter . . . 11

2.6 About ATMEL AVR AT90CAN128 . . . . . . . . . . . . . . . . . . . . . 12

2.7 Lab Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter 3: FFT Algorithm and frequency spectra 17

3.1 Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 FFT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Frequency Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chapter 4: Implementation 25

4.1 INPUT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 EXECUTION FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 OUTPUT FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 DETECT FREQ Function . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.5 Program to detect velocity data . . . . . . . . . . . . . . . . . . . . . . . 28

4.6 Program to convert float64 to float32 . . . . . . . . . . . . . . . . . . . . 29

Chapter 5: Results 31

Chapter 6: Future Work 35

Chapter 7: Conclusion 37

Appendix A:Code - Main function 39

Appendix B:Code - Macros 43

Appendix C:Code - Function Description and constant tables 47

Appendix D:Code - Flow Meter data filtering 55

Appendix E:Code - Covert float64 to float32 57

viii

List of Figures

2.1 A D-Flow ultrasonic flow meter with a longitudinal configuration. . . . . 8

2.2 A D-Flow ultrasonic flow meter with a diagonal configuration. . . . . . . 8

2.3 Detection of a pulsating flow by Hinich’s harmogram (simulation) . . . . 13

2.4 Detection of a pulsating flow by Hinich’s harmogram (real signal) . . . . 13

2.5 Atmel AVR AT90CAN128 Micro-controller connected with STK500, used

for this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Butterfly signal flow graph . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Successive steps in an 8-point FFT . . . . . . . . . . . . . . . . . . . . . 21

3.3 Successive steps in an 8-point FFT (continuation) . . . . . . . . . . . . . 22

4.1 Flow diagram of implementation for detection of pulsating flow. . . . . . 26

4.2 Packet received by serial port of micro-controller . . . . . . . . . . . . . . 28

5.1 Welch method’s output for y = 5×sin(2×π×50×t)+10×sin(2×π×200×t)

signal (Matlab simulation). . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Welch method’s output for previous signal corrupted by zero-mean random

noise (Matlab simulation). . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Welch method’s output for Berrebi’s data (Matlab simulation). . . . . . . 33

6.1 Future implementation for M-16 based Ultrasonic Flow Measurement. . . 35

1

CHAPTER 1

Introduction

1.1 Introduction

Accurate measurement is an important factor in District Heating Industries as annual cost

of total metering error is approximately estimated 170 Millions of Swedish Crowns for the

Swedish District Industries. These industries supply hot water in buildings and houses

through a network. The energy supplied to a customer is measured by thermometers and

by a flow meter inside the district-heating substation, which are present at the customer’s

place.

Among the flow meters, the Transit-time Ultrasonic flow meters are accepted as a

great interest as they are accurate, non-intrusive and cheap but they are very sensitive

to installation effects1 and other source of errors. Installation effects could be either

static or dynamic. A pulsating flow is a dynamic installation effect. In 2001, Carlan-

der stated in his PhD thesis that pulsating flows generate harmonic structure in the

frequency spectrum of the measured flow velocity [1] and he investigated the possibility

of self-diagnostic techniques for flow meters. Berrebi introduced and implemented the

idea of self-diagnosing technology, which can detect the pulsating flow by using Hinich’s

harmogram [2]. However, he implemented it in MATLAB and it requires powerful com-

puter, which was expensive. This was one of the drawbacks to install his implementation

industrially.

Recently, in competitive market, micro-controllers have become very cheap and they are

capable to do complex computations as they are faster and have relatively high storage

capacity. Therefore, it is of great interest to implement self-diagnosis techniques to error

1Installation effects are the performance deviations from the calibration lab due to the environmentin which the sensor or meter is installed.

3

4 Introduction

reduction for ultrasonic flow measurement in a micro-controller. It will be exceptionally

inexpensive and economically beneficial for an industry.

In this thesis, the ATMEL AVR micro-controller have used to receive the serial input

from Transit-time ultrasonic flow meter and detect pulsating flow from the flow velocity

data. Fast Fourier Transform (FFT) and absolute value of it, i.e. the frequency spectra,

have been implemented in the AVR to detect pulsating flow that Berrebi did in Matlab

and serial communication is also implemented to receive velocity input data. Experimen-

tal data have been used and results are shown which are generated by micro-controller

and perform comparison with Matlab simulations. It shows exactly the same results as

the results in Matlab calculations. Therefore, Matlab and a Laptop can be replaced by

the micro-controller already present in flow or heat meters, to detect the pulsating flow,

which fulfill the commercial use of Berrebi’s work.

CHAPTER 2

Background

2.1 Flow meters summary

Flow meters are used to measure flow rate. There are several types of flow meters with

different measuring methods. In this section, the most common industrially used flow

meters are described briefly and some of them are also commonly used in the district

heating sub-station. At close to ideal condition, accuracies of ±0.5% or slightly better

can be achieved for some types of flow meters. Rangeabilities of 1:100 and more can also

be achieved [3].

2.1.1 Differential pressure flow meters

These flow meters have been most commonly used flow rate measurement device in

industry and have about 40% of the market [4]. The orifice plate is the most excepted

and widely used among the different types of DP flow meters. All DP flow meters have

almost the same operation principles. According to Bernoulli’s equations, a change in

cross section area of flow meter causes a change in velocity and pressure. The flow rate

can be expressed as a function of the difference in pressure in larger and smaller cross

section area, by using continuity equation. The orifice flow meter uses a plate with a hole

smaller than the cross section area of the pipe for the flow restriction. The pressure of

upstream and downstream of the plate is measured by a differential pressure transmitter.

The orifice flow meter is affected by installation effect. The error will be caused by

disturbed velocity profiles and swirling flow [5].

• The advantages and disadvantages of the orifice flow meter [3].

– Simple and robust design but low range ability.

5

6 Background

– It has well established standards but sensitive to coating on the plate.

– It requires no calibration for standard design, however it is sensitive to instal-

lation effects.

2.1.2 Variable area flow meter

‘Rotameters’ are the most commonly used type of variable area flow meters. Variable

area flow meters have industrial use of more than 10% among the flow meters [4]. Its

working principle is different than the DP flow meter. In this meter, the differential

pressure remains constant and the flow is measured as a function of the reduction is area.

This area is generally displayed by the position of a freely moving float producing the

variable area. A float with a density greater than the fluid is used in the ‘Rotameters’

type. It is placed in a vertical conical tube with the wider end pointing up. The float

is lifted by the flow until the balance is reached between gravitational, buoyancy and

hydrodynamic forces. The flow rate is indicated by the position of the float and it is

sensed by a magnetic pickup and also can observed directly if the tube is transparent [3].

• The advantages and disadvantages of the ‘Rotameters’ flow meter.

– Simple design but moderate accuracy and it must be mounted vertically.

– Its price is low.

– It is insensitive to static installation effects but sensitive to pulsating flow.

2.1.3 Electromagnetic flow meters

District heating companies in Sweden, commonly use electromagnetic or magnetic induc-

tive (mag or MID) flow meters. More than 30% of the meters are of this types [6]. In

general, industrial use of MID flow meters is less than 10% [4]. MID flow meters oper-

ate on the principles of Faraday’s law of electromagnetic induction, therefore, they are

designed to measure the velocity of electrically conductive liquids. A velocity is induced

when a conductor is passed through a magnetic field. The fluid acts as a conductor in

the MID flow meters and a magnetic field is generated by magnetic coil. This coil is

mounted on the outside of a non-magnetic pipe segment. Two electrodes are used to

detect the induced voltage [7]. This flow meter is generally less sensitive to installation

effects than many other flow meter types.

• Some advantages and disadvantages of the MID flow meter are outlined below [3].

– It has good accuracy but the fluid must be conductive.

– There is no moving part but deposit inside the meter can cause errors in the

output (e.g. copper sediment from copper pipes).

– Low-pressure loss.

– Not significantly effected by moderate profile distortions.

2.2. Transit-Time Ultrasonic Flow Meters 7

2.1.4 Mass flow meter

The mass flow is directly measured by this group of flow meters, whereas other flow

meters have to measure density in order to deliver mass flow, therefore sensitive to change

in temperature and pressure. Among the Mass flow meters, Coriolis type is the most

commonly used mass flow type and industrially has more than 5% use of this flow meter

[4].

When a body is rotated about a fixed point and changes its position relative to that

fixed point, the coriolis force is generated. Forcing the pipe to vibrate, Coriolis forces

are generated in this meter. Normally, a U-bend pipe is forced to vibrate in the middle

and anchored at the ends. When a fluid passes through the pipe, Coriolis forces will

be generated in opposite directions in each half of the U-bend. This force the U-bend

to twist. The two halves of the U-bend pipe will then pass a fixed plane at different

times. This time difference is directly related to the mass flow through the pipe [8]. A

weight vector theory can apply to compensate for the velocity distribution effects inside

the pipe. This mass flow meters are known as insensitive to installation effects.

• Some advantages and disadvantages of the Coriolis flow meters are sketched below

[3].

– It has Wide rangeability but pressure drops may be high.

– High accuracy but Zero flow accuracy may be low.

– Low-pressure loss.

– Operates on virtually every fluid but the price is high.

2.2 Transit-Time Ultrasonic Flow Meters

In industrial applications, the transit-time or sing-around flow meter is widely used. This

is the most commonly used type [4]. This method was first issued by Rutten in 1931 [9].

Transit-Time ultrasonic flow meter measures the time difference for the sound to travel

between two transducers. One transducer is placed upstream and other relatively more

downstream. From both directions, the times of flight are measured. The interaction of

the fluid velocity makes the upstream time of flight longer then the downstream. The

fluid velocity is proportional to the difference between the two inverted times of flight.

The sing-around flow meter works in the frequency domain. The basic operations are

similar for the transit-time and the sing-around flow meter but instead of measuring the

time, a pulse is send continuously in a frequency and measured. Therefore, the transit-

time performs only one single sound transmission in each direction. But the sing-around

method uses multiple loops. Thus, the sing-around flow meter produces much better

time resolution. When small flow rates are measured this operation is useful as the time

8 Background

Transducer

FLOW

FLOWMETER BODY UPSTREAM DOWNSTREAM

Figure 2.1: A D-Flow ultrasonic flow meter with a longitudinal configuration. The diameter inthe metering section is 9 mm [1].

23,5 mm

48 mm

10 m

m

18,9

mm

inle

t

ou

tlet

upstreamtransducer

downstreamtransducer

ultrasonic beam

flow

Figure 2.2: The diagonal configuration. The diameter in the metering section is 10 mm [1].

2.3. Problems of Ultrasonic Flow Meters 9

difference between the up- and downstream measurements is very short. The velocity is

now proportional to the difference between the down- and upstream frequencies [10].

The flow velocity calculation algorithm does not include the speed of sound. The

flow velocity only depends on the difference between the upstream and downstream sing-

around frequencies [11]. By using the four latest determined frequencies, the performance

of the meter can be improved and calculate the flow velocity as running average [12]. The

number of loops used to determine each frequency also influences the performance [13].

There are no limits in size in ultrasonic flow meter. Measurement has also presented

using diameter of a pipe more than 5 m [14]. The ultrasonic transit-time flow meters are

sensitive for installation effect. Because the flow is measured between transducers instead

of the entire cross section area, the sensitivity to disturbed flow profiles increase as the

dimension of pipe and meter grows and ratio between the diameter of the transducer and

diameter of the pipe decreases [3]. On the previous page, two implementation of transit-

time ultrasonic flow meters are depicted in figure 2.1 and 2.2. Ultrasonic flow meter are

not widely used in Swedish district heating distribution systems. But in Denmark the

use of ultrasonic flow meter are more common. 80% of the meters are of this type in

their district heating systems [16].

• Some advantages and disadvantages are mentioned below [3].

– It is none intrusive - low pressure drop and can be used directly on the pipe.

– Good accuracy and no limit in size but sensitive to installation effects.

2.3 Problems of Ultrasonic Flow Meters

The performance of any flow meter will vary significantly between experimental results

in laboratory and real life implementation. For example, thermometers indicating the

outside temperature are usually placed close to the house in order to be readable from

the house, but the closeness of the house influences the thermometer. In winter, the

house generates heat and its neighbourhood is warmer than any other place outside.

Therefore, the indicator will show higher temperature than original outside temperature.

This is an example of installation effect. There are two types of installation effects -

Static installation effect and Dynamic installation effect.

2.3.1 Static installation effects

The effects that do not change with time are called static installation effects [3]. Some

of the static effects are:

• Single and double elbows

• Diameter reduction

10 Background

• Partially open valve

• Bluff bodies (thermometers, etc.)

These can be grouped into two categories; those that distort the flow profile but produce

little swirl and those that distort the flow profile but cause bulk swirl. Single elbow pipe

bend is the example of the first category and the second category can be exemplified by

the double elbow mounted out of plane.

2.3.2 Dynamic installation effects

Effects that arise from rapid time dependent changes in the flow field or by pulsation in

the flow are called Dynamic installation effects. It was investigated by Lindahl in 1946

[17] and by Mottram in 1992 [18]. These effects can be caused by pumps and compressor,

control valves and pressure regulators or by flow-induced oscillations. The profile of the

velocity field will be changed by the pulsations and make it time dependent [19]. Both

these effects can cause errors in the flow measurements.

2.4 Carlander’s Self Diagnostics for Ultrasonic FlowMeasurement

Carlander, in his PhD thesis Installation Effects and Self-Diagnosis for Ultrasonic Flow

Measurement, illustrates that it is possible to detect effects due to installation by analyz-

ing the measurement noise [1]. His experimental results demonstrate not only that the

installation effects tested introduce errors in the flow measurements but also that these

effects can be detected from the noise level in the data. The noise level was determined

from the standard deviation. This could be interpreted as that the disturbances amplify

the turbulence intensity. Thus, the standard deviation can be used as a measure of the

turbulence. The presence of a disturbance could be recognized by comparing the magni-

tude of the noise level in the present data with a reference level valid for the measured

flow rate. A procedure like this could possibly be performed by the meter itself in oper-

ation [15]. Therefore, a diagnostic procedure could be introduced in the flow meter and

it is called self-diagnostic techniques.

Carlander used five different test configurations i.e. a reference experiment, a single

elbow, a double elbow out of plane, a reduction in pipe diameter and a pulsating flow

experiment. He also explained different types of flow meter and comparison between

them, their advantages and disadvantages.

2.5. Berrebi’s Detection of Pulsating Flows in an Ultrasonic FlowMeter 11

2.5 Berrebi’s Detection of Pulsating Flows in an Ultra-sonic Flow Meter

Earlier it is mentioned that Ultrasonic Flow Meter is sensitive to installation effect and

installation effect can be either static or dynamic. A pulsing flow is a dynamic installation

effect and for experimental purpose it can be generated by pump. In the practical

environment, diagnostic can only be performed with the measured flow rate. In Berrebi’s

experiment he recorded flow measurement with and without pulsating flow in the flow

meter calibration facility and detect the pulsating flow using Hinich’s harmogram. It is

possible to detect harmonics that emerge from the noise by using the harmogram [2].

The description is as follows:

According to [20], a steady flow rate is the superposition of a constant flow umean and

some variation u(t) around the mean flow rate:

u(t) = umean + u(t). (2.1)

When pulsations are added to u(t), the instantaneous flow velocity can be written as:

u(t) = umean(1 + a · sin(2πfpulst)) + u(t), (2.2)

where a is the amplitude of the pulsations of the frequency fpuls. The object to be

detected is then the amplitude of the pulsations drawn in the noise. Therefore, the

constant flow umean is useless for processing the signal. We can then focus on the signal

v(t) that is the dynamic part of u(t) [2]:

v(t) = umean · a · sin(2πfpulst) + u(t). (2.3)

Therefore, pulsations generate sampling error and error due to velocity profile vari-

ations. In the experiment of Berrebi, the sampling error is neglected since the error

computed is not instantaneous, but average over 1000 samples. Instantaneously, the

sampling error Es(t) is due to the sinusoidal component of the pulsating flow:

Es(t) = umean · a · sin(2πfpulst). (2.4)

Taking the average of Es(t) over time T gives:

1

T·∫ T

0

Es(t) =umean · a · (1− cos(2πfpulst))

2πfpulst. (2.5)

The limit of the latter quantity is zero when T 1\fpuls. Therefore, the integration over

a long time interval of the flow meter error cancels the sampling error. It is then mainly

the error due to the velocity profile variations that is shown in [20].

Applying Jarque-Bera test on u(t), it is verified that u(t) is Gaussian Distributed

[21]. Let Sp(f) be the estimation of the power Spectral density (P.S.D.) of u(t) via the

periodogram on a certain time interval. Therefore,

12 Background

Sp(f) = |U(f)|2, (2.6)

where U is the Fourier transform of u. Let Sw(f) be a previous and more accurate

estimation of the P.S.D. via Welch’s method (averaged periodogram), then:

Sw(f) =1

W·

∑Wintervals

|U(f)|2, (2.7)

where W is the length of the moving average used in the P.S.D. estimation via Welch’s

method. In [22], it is describe that the gaussian assumption implies that the ratio H(f)

= Sp(f)

Sw(f)(Hinich’s harmogram for detecting the presence of one harmonic only) follows a

χ2 distribution with two degree of freedom. This quantity has then a high probability to

vary within the interval [1 - W−1/2, 1 + W−1/2]. An α−test level provides a threshold Tα

for the quantity H(f). If maximum item between H(f) and any frequency f between 0

to fs/2 is greater than Tα, i.e., max H(f), f ∈ [0, fs/2] > Tα] (where fs is the sampling

frequency), then a harmonic is detected. Pulsating flows not only generate harmonics in

the P.S.D., but also increase the noise level. The background noise of the pulsating flow

cannot be estimated alone (without harmonics). Thus a good estimation of background

noise in required to determine the value of the threshold Tα function of the noise level.

Berrebi ran the harmogram first on a mixed real-synthetic signal v(t) that is the sum of

the reference flow rate’s background noise uREF (t) from the first experiment and synthetic

sinusoid of frequency fpuls = 5 Hz whose amplitude is 0.1 times the mean flow uREFmean:

v(t) = uREFmean · 0.1 · sin(2πfpulst) + uREF (t). (2.8)

The result is shown in Figure 2.3. The maximum amplitude of the harmogram is above

the threshold at 5Hz. A pulsating flow is detected. Secondly, the harmogram is applied

to a real pulsating flow obtain during the experiments. The estimation of the background

noise is required for detecting harmonics in the signal. The results of the harmonics are

shown in Figure 2.4. A fundamental and its harmonics are above the threshold Tα around

9Hz, 18Hz and 27Hz. A Pulsating flow is then detected [2].

Therefore, It is depicted clearly that Berrebi used Matlab and described pulsating flow

in harmogram. It required implementation of FFT in Matlab. To implement his work in

micro-controller, it is also essential to implement FFT in micro-controller. The following

sections will describe this key part.

2.6 About ATMEL AVR AT90CAN128

In the Embedded Electronics project course at Lulea University of Technology, the AT-

MEL AVR AT90CAN128 micro-controller is used for the electronic part to build Formula

Student Race Car. Therefore, it is available at EISLAB and also used for this thesis. Im-

2.6. About ATMEL AVR AT90CAN128 13

Figure 2.3: Detection of a pulsating flow by Hinich’s harmogram (simulation) [2].

Figure 2.4: Detection of a pulsating flow by Hinich’s harmogram (real signal) [2].

14 Background

plementations on an 8-bit micro-controller also ensure the possibility to implement it on

a 16-bit micro-controller. Therefore, This 8-bit ATMEL AVR is used.

It is based on the AVR enhanced RISC architecture and a low-power CMOS 8-bit

micro-controller. The AT90CAN128 achieves throughput approaching 1 MIPS per MHz

and execute powerful instructions in a single clock cycle that helps the system designer

to optimize power consumption versus processing speed. Some important features are

mention below:

• 133 mostly single cycle instructions and performance 16 MIPS @ 16MHz.

• 32 general-purpose registers, all are directly connected to the Arithmetic Logic Unit

(ALU).

• 128K bytes of In-System Programmable Flash with Read-While-Write capabilities.

Endurance: 10,000 Write/Erase Cycles.

• 4K bytes EEPROM.

• 4K bytes SRAM.

• On-chip 2-cycle Multiplier. This is an essential feature for this thesis.

• 53 general-purpose I/O lines.

• Real Time Counter (RTC), four flexible Timer/Counters with compare modes and

PWM.

• Dual Programmable Serial USART.

• An 8-channel 10-bit ADC with optional differential input stage with programmable

gain.

• A programmable Watchdog Timer with Internal Oscillator.

• IEEE std. 1149.1 compliant JTAG test interface, used for accessing the On-chip

Debug system and programming.

• 5 Sleep Modes: Idle, ADC Noise Reduction, Power-save, power-down & Standby.

• Operating Voltages - 2.7 - 5.5V

2.7. Lab Setup 15

Figure 2.5: Atmel AVR AT90CAN128 Micro-controller connected with STK500, used for thisthesis.

2.7 Lab Setup

The flow meter calibration facility at Lulea University of Technology is performed with

a calibrated rig. The rig has an accuracy of ±0.1% at flow rate over 20 l/h. The

determination of flow is based on continuous weighing [15]. D-flow generates that flow

velocity values using 64-bit floating-point numbers. To use those data in Atmel AVR and

for faster calculations, it is important to convert them to 16-bit integer.

CHAPTER 3

FFT Algorithm and frequencyspectra

3.1 Fast Fourier Transform

Suppose, x(t) is a signal and X(ω) is the Fourier transform of x(t). If x(nT ) and X(rω0)

are the nth and rth samples of x(t) and X(ω), respectively, then we define new variables

xn and Xr as

xn = Tx(nT ) =T0

N0

x(nT ) (3.1)

and

Xr = X(rω0), (3.2)

where

ω0 = 2πf0 =2π

T0

(3.3)

Therefore, xn and Xr are related by the following equations [23]:

Xr =

N0−1∑n=0

xne−jrΩ0n (3.4)

xn =1

N0

N0−1∑r=0

XrejrΩ0n, (3.5)

17

18 FFT Algorithm and frequency spectra

where Ω0 = ω0T = 2πN0

and N0 is the number of samples of the signal. These equations

define the direct and the inverse discrete Fourier transforms, with Xr the direct discrete

Fourier transform (DFT) of xn, and xn the inverse discrete Fourier transform (IDFT) of

Xr. The notation

xn ⇐⇒ Xr

is also used to indicate that xn and Xr are a DFT pair [23].

Now, we can simulate 4-point FFT with the following Matlab code:

t = 0: 1/1000: 3/1000; % Sampling time

y = sin(2*pi*60*t); % Signal x(t)

N0 = 4; % Number of samples in the signal

for r = 0:3 % rth sample of X(w)

fft_y = 0;

for n = 0:3 % nth sample of x(t)

fft_y = fft_y + y(n+1)* exp(-j* r * (2*pi/N0) *n);

end

fft_y

end

The above codes execute the operation of fft function of Matlab for signal y = sin(2 ∗π ∗ 60 ∗ t) and give the output X0 = 1.9575, X1 = −0.6845 + 0.5367i, X2 = −0.5884,

X3 = −0.6845− 0.5367i. Therefore, it is clear that we need addition and multiplication

operation to implement the FFT. Now, the FFT Algorithm is described in the following

section.

3.2 FFT Algorithm

From Equation (3.4) to compute one sample Xr, it is required N0 complex multiplication

and N0 − 1 complex additions. To compute N0 such values (Xr for r = 0,1,...,N0 − 1),

it is required a total of N20 complex multiplication and N0(N0 − 1) complex addition.

Therefore, for a large N0, these computations can be prohibitively time-consuming, even

for a high-speed computer. In 1965, Cooley and Tukey developed the algorithm, known

as the Fast Fourier Transform that reduces the number of computations from something

on the order of N20 to N0logN0. The number of computations in performing the DFT

was dramatically reduced by this algorithm.

The secret is in the linearity of the Fourier transform. Because of linearity, we can

compute the Fourier transform of a signal x(t) as a sum of the Fourier transforms of

3.2. FFT Algorithm 19

segments of x(t) of shorter duration. Consider a signal of length N0 = 16 samples. As

seen earlier, DFT computation of this sequence requires N20 = 256 and N0(N0 − 1) =

240 additions. We can split this sequence in two shorter sequences, each of length 8.

To compute DFT of each of this segments, we need 64 multiplications and 56 additions.

Thus, we need a total of 128 multiplications and 112 additions. Suppose, we split the

original sequence in four segments of length 4 each. To compute DFT of each of this

segments, we require 16 multiplications and 12 additions. Thus, we need a total of 64

multiplications and 48 additions. If we split this sequence in eight segments of length 2

each, we need 4 multiplications and 2 additions for each of the segment resulting a total

of 32 multiplications and 8 additions. Therefore, we have been able to reduce the number

of multiplications from 256 to 32 and the number of addition from 240 to 8. Moreover,

some of these multiplications turn out to be multiplications by 1 or −1. Thus, we can

realize the economy of FFT without any approximation. The value obtain by the FFT

are identical to those obtained by DFT. The reduction in number of computations is

much more dramatic for higher value of N0.

The FFT algorithm is simplified if we choose N0 to be a power of 2. For convenience,

it is defined that

WN0 = e−(j2π/N0) = e−jΩ0 (3.6)

so that

Xr =

N0−1∑n=0

xnWnrN0

0 ≤ r ≤ N0 − 1 (3.7)

Although there are many variations of the Tukey-Cooley algorithm, here is described the

decimation in time algorithm.

In this algorithm we divide the N0-point data sequence xn into two (N0)/2-point se-

quence consisting of even- and odd-numbered samples, respectively, as follows:

x0, x2, x4, ...., xN0−2︸︷︷︸sequence gn

, x1, x3, x5, ...., xN0−1︸︷︷︸sequence hn

Then, from Equation (3.7),

Xr =

(N0/2)−1∑n=0

x2nW2nrN0

+

(N0/2)−1∑n=0

x2n+1W(2n+1)rN0

. (3.8)

Also, since

WN0/2 = W 2N0

, (3.9)

we have


Figure 3.1: Butterfly signal flow graph [23].

Xr =

(N0/2)−1∑n=0

x2nWnrN0/2 + W r

N0

(N0/2)−1∑n=0

x2n+1WnrN0/2 (3.10)

= Gr + W rN0

Hr 0 ≤ r ≤ N0 − 1 (3.11)

where Gr and Hr are the (N0/2)-point DETs of the even- and odd-numbered sequences,

gn and hn, respectively. Also, Gr and Hr, being the (N0/2)-point DETs, are (N0/2)

periodic. Hence

Gr+(N0/2) = Gr and Hr+(N0/2) = Hr. (3.12)

Moreover,

Wr+(N0/2)N0

= WN0/2N0

W rN0

= e−jπW rN0

= −W rN0

. (3.13)

From Eqs. (3.11), (3.12) and (3.13), we obtain

Xr+(N0/2) = Gr −W rN0

Hr. (3.14)

This property can be reduce the number of computations. We can computer the first

N0/2 points 0 ≤ n ≤ (N0/2)− 1 of Xr by using Eq. (3.11) and the last N0/2 points by

using Eq. (3.14) as

Xr = Gr + W rN0

Hr 0 ≤ r ≤ N0

2− 1 (3.15)

Xr+(N0/2) = Gr −W rN0

Hr 0 ≤ r ≤ N0

2− 1 (3.16)

Thus, an N0-point DFT can be computed by combining the two (N/2)-point DFTs, as

in Eqs. (3.15) and (3.16). These equations can be represented conveniently by the signal

flow graph depicted in Fig. 3.1. This structure is known as butterfly. Figure 3.2 shows

the implementation of Equs. (3.12) for the case of N0 = 8.

The next step is to compute the (N0/2)-point DFTs Gr and Hr. We can perform it by

continuing the same procedure by dividing gn and hn into two (N0/4)-point sequences

3.2. FFT Algorithm 21

Figure 3.2: Successive steps in an 8-point FFT [23].

corresponding to the even- and odd-numbered samples. Then we repeat this process until

we reach the one-point DFT. These steps for the case of N0 = 8 are shown in Fig. 3.2,

Fig. 3.3 shows that two-point DFTs require no multiplication.

To count the number of computations required in first step, assume that Gr and Hr are

known. Equations (3.15) and (3.16) clearly shows that to compute all the N0 points of the

Xr, we require N0 complex additions and N0/2 complex multiplications corresponding

to W rN0

Hr.

In the second step, to compute the (N0/2)-point DFT Gr from the (N0/4)-point DFT,

we require N0/2 complex additions and N0/4 complex multiplications. We require same

number of computations for Hr. Hence, in the second step, there are N0 complex addi-

tions and N0/2 complex multiplications. The number of computations required remains

the same in each step. Since a total of log2N0 steps is needed to arrived at a one-point

DFT, we require, conservatively, a total of N0log2N0 complex additions and (N0/2)log2N0

complex multiplications, to compute the N0-point DFT. Actually, as Fig. 3.3 shows,

many multiplications are multiplications by 1 or -1, which further reduces the number of

computations.

Another FFT algorithm, the decimation-in-frequency algorithm, is similar to that of

decimation-in-time algorithm. The only difference is that instead of dividing xn into two

sequences of odd- and ever-numbered samples, we divide xn into two sequences formed

by the first N0/2 and the last N0/2 digits, proceeding the same way until a single-point

DFT is reached in log2N0 steps. The total number of computations in this algorithm is


Figure 3.3: Successive steps in an 8-point FFT (continuation) [23].

the same as that in the decimation-in-time algorithm [23].

The following chapter will describe the functions input(), execution() and output() that

are written for FFT and PSD in the micro-controller.

3.3 Frequency Spectra

The frequency spectra of a continuous-time system are represented by frequency plots

of the magnitude and phase of its transfer function. Since the system transfer function

for a given frequency is a complex number, its magnitude and phase (angle) depend on

frequency; that is,

H(jω) = ReH(jω)+ jImH(jω) = |H(jω)|ej]H(jω)

|H(jω)| =√

(ReH(jω))2 + (ImH(jω))2 (3.17)

3.3. Frequency Spectra 23

]H(jω) = tan−1

(ImH(jω)ReH(jω)

)Here, H(jω) is called system transfer function. Plotting |H(jω)| and ]H(jω) in terms

of frequencies ω produces the system magnitude and phase spectra [24]. Many useful

results can be obtained by studying the shapes of the magnitude and phase spectra.

The magnitude and phase spectra are very important for communications and signal

processing.

CHAPTER 4

Implementation

In this sections, the micro-controller implementation of the FFT is described. A Mixing

of C and assembly is used to get faster output and the AVR GCC 3.4.3 compiler is used.

The main three functions are implemented in assembly to make the program faster. To

construct 16-bit operations, macros are used and those macros perform 16 bit operations

using AVR Assembler’s instructions set. addd and subd macros perform 32-bit addition

and substraction. AVR Assembler User Guide is a key data sheet for this implementation

[25]. Hyper terminal is used to display data. The flow diagram of the implementation is

depicted in Fig. 4.1 on next page.

4.1 INPUT FUNCTION

fft input() fills the complex array bfly Array with the velocity data to prepare butterfly

operations. A hamming window is applied at the same time. When fft input(flowInput,

bfly Array) is called the first parameter, flowInput is addressed by r25:r24 register and

second parameter, bfly Array is addressed by r23:r22 register. tbl window array con-

tains the data of Hamming window. Hamming window is generated using the following

equation [26] and multiply all data with 32767 value generated by that equation.

ω(n) = 0.54− 0.46 cos

(2πn

N − 1

)Some of the properties of the DFT that can lead to incorrect results can be improved

by using a windowing function on the data. These functions smoothly tail off the signal

at both ends, reducing DFT leakage. Each point in the signal is multiplied by a window

scaling factor before the FFT is calculated. The code is given in the Appendix C.

The input data for FFT that is generated by flow meter is 64-bit floating-point num-

ber. As AVR AT90CAN128 has 4K bytes SRAM, to compute 512-point FFT, it is not

25

26 Implementation

Figure 4.1: Flow diagram of implementation for detection of pulsating flow.

sufficient. Moreover, AVR does not support 64-bit floating-point number. Therefore, it

is essential to convert it in 32-bit floating-point number and for faster calculation floating

point number is converted to 16-bit integer. But flow meter data is quite lower valued

(about -40.00 to +45.00), as sampling rate is low. A lot of real values like 0.8 or 0.1 will

be 0 if they are transferred directly to integer. Therefore, before transformation, all real

values are first multiplied by 1000. That does not effect the calculation of FFT.

4.2 EXECUTION FUNCTION

The implemented algorithm can support 512, 256, 128, 64-point FFT algorithm and it

can also support complex number input. However, 512-point FFT is used for flow meter

4.3. OUTPUT FUNCTION 27

data as 512-point FFT is more accurate than the other three, however it will occupy

more program memory about 512 × 2 = 1024 bytes for input sampled data. The flow

meter samples the data in 64-bit floating-point number. Therefore, this data can handle

using integer array. It will be described later in this section.

The most important instruction in this function is FMULS16 which is 16-bit floating

point signed multiplication and generates 32-bit number. It is also possible to implement

multiplication operation using left shift operation and addition but it will take more clock

cycles in the micro-controller. Without using FMULS16, the 16× 16-bit multiplication

on a AT90CAN128 will require 4, 8-bit multiplies and then 4, 8-bit additions. Therefore,

multiplication can be done with a series of additions and shifting. The fastest way to

do this will be 8, 16-bit shifts, and 8, 16-bit adds. Thus, (8 + 8 × 2 + 8 × 2) = 40, 8

bit operations, i.e., 40 clock cycles are needed at minimum by using shifting operation,

because 8-bit add and shift operations take one cycle in AT90CAN128.

However, in section 2.6, it is described that AT90CAN128 has an advantage that can

perform on-chip 2-cycle 8-bit multiplication and generates 16-bit value. These instruc-

tions, FMUL and FMULS reduce the clock cycles and for 16 bit multiplication it will

take 19 clock cycles. The code is given in the Appendix.

In section 3.2, the FFT operation is described and following through that description,

we can find that for 512-point FFT, 256× 4 = 1024, 16-bit multiplications and 256× 2

= 512, 16-bit additions are required. Therefore, 1024×19+512×2 = 20480 clock cycles

i.e 20.48 milliseconds will take at minimum condition.

In this function, cosine and sine table are also used to make the calculation faster. This

values will be stored in program memory of the controller. The butterfly operation is

performed in this function.

4.3 OUTPUT FUNCTION

After butterfly operation using fft execute() function, it is required to find frequency

spectra to plot the data and need to verify the pulsating flow. To do this, fft output()

function performs the operation that is described in section 3.3. Execution function

constructs data in real and imaginary values. Output function squares those real and

imaginary parts and sum them together, then square-roots the resultant value. Square-

root macro receives 32-bit data and takes 526 to 542 clock cycles depending on data.

This construct the absolute values of Fourier transform and those data can be plotted to

find the pulsating flow.

4.4 DETECT FREQ Function

This function detects the pulsating frequency from the Fspectra array. Fspectra array

contains the data of frequency spectra that are generated by fft output function. This

28 Implementation

code is written in C. Simulating different data, it is found that if any pulsating frequency

exists then that can be detectable by scanning three consecutive data. If any of consecu-

tive three values are greater than the average value in the Fspectra array then a frequency

is found. The maximum value of those three data can also be found. The position of this

maximum value is multiplied with sampling frequency and divided by N-point FFT to

get the desired frequency. Max function is used to get the maximum value of three data.

4.5 Program to detect velocity data

The flow meter data are filtered by singnal.c subroutine to get flow velocity data. Figure

4.2 describes a packet, which is received by serial port of the micro-controller.

Figure 4.2: Packet received by serial port of micro-controller (Values are in Hexadecimal).

The packets that micro-controller receives, has starting bytes and ending bytes with

0x10, 0x02 and 0x10, 0x03 respectively. After starting bytes, there are three reverse

bytes and those contains data depending on the scripts running in the flow meter. The

flow velocity data is found after those reserved bytes. This data is generated as 64-bit

floating-point number by flow meter. The Flow meter transmits that data in 8 bytes.

However, if any byte contains 0x10 value then flow meter produces another 0x10 value

in the next byte. The reason is to distinguish that value from start and end bytes.

Therefore, when we will filter a packet, we have to check the sequential duplication of

0x10 values in the packet. If it is found then we need to make it a single 0x10 value. It

is also important to observe that if there is a 0x10 value in the velocity data then for

duplicate 0x10 value, there will be total 9 bytes for flow velocity data. Moreover, there

can be more extra bytes depend on 0x10 values in the velocity data. But we have to filter

8 bytes from those bytes. The signal.c program describes an algorithm to filter those

desire 8 bytes flow velocity data. It uses an infinite while loop because 0x10 value can

be more than one and that is undefined. The code to filter this actual 8 bytes is given in

the appendix D.

4.6. Program to convert float64 to float32 29

The 8 bytes data that are filtered, should be read in opposite direction. Therefore, in

signal.c program data are stored from the bottom of the array so that first index contains

the starting byte of the 64-bit value.

4.6 Program to convert float64 to float32

ATMEL AVR Micro-controller does not support 64-bit float point number but it support

32-bit. Moreover, if floating-point numbers are used for calculation then it will take

double memory than an integer in data memory and that is expensive. Therefore, 64-

bit float point number is converted, first in 32-bit floating-point number where only the

integer part is used for FFT operation. Float64 to float32 program does this operation.

The 64-bit float point number is called IEEE double precision floating point standard

and 32-bit float point number is called IEEE single precision floating point standard.

The following table shows the layout for single (32-bit) and double (64-bit) precision

floating-point values. The number of bits for each field is also shown (bit ranges are in

square brackets):

Sign Exponent Fraction Bias

Single Precision 1 [31] 8 [30-23] 23 [22-00] 127

Double Precision 1 [63] 11 [62-52] 52 [51-00] 1023

Therefore, for conversion 11 bits of exponential part should be transferd in 8 bits and

52 bits fractional part should be transfer in 23 bits. In this, program left and right shift

and bias are used to perform it. First, 8 bits of 11 in exponential part and 23 bits of 52

bits in fractional part are taken and in exponential part bias 1023 is deducted and 127 is

added. This produce the 32-bit float and become almost same number that flow meter

sends. The code is shown in the appendix E.

CHAPTER 5

Results

In this section, different signals are used in Matlab and micro-controller. PWELCH

(Power Spectral Density estimate via Welch’s method) function is used to detect the

frequency in Matlab. Those signals are also used as the input of FFT in Micro-controller,

to detect the frequency then compare them with Matlab’s outputs. It shows exactly the

same result in both cases. First, y = 5× sin(2× π × 50× t) + 10× sin(2× π × 200× t)

signal’s Matlab result is shown in figure 5.1.

Figure 5.1: Welch method’s output for y = 5× sin(2× π × 50× t) + 10× sin(2× π × 200× t)signal (Matlab simulation).

31

32 Results

The Matlab code is as follows:

t = 0:0.001:300;

t = t(1:512);

y = 5 * sin(2*pi*50*t) + 10 * sin(2*pi*200*t);

y = y + abs(min(y));

y = y / max(y);

y = 1000 * y;

pwelch(y,window(@hamming,512),[],512,1000);

When this signal is used as input in Micro-controller, it detects peaks at 50.7813 Hz

and 199.2188 Hz. Therefore, an accurate performance is figured out by micro-controller.

In the next example, The same signal is used but some zero-mean random noise is used

to corrupt it. A common use of Fourier transforms is to find the frequency components

of a signal buried in a noisy time domain signal. By using Matlab’s PWELCH function,

the result is shown in figure 5.2.

Figure 5.2: Welch method’s output for previous signal corrupted by zero-mean random noise(Matlab simulation).

The Matlab code is as follows:

t = 0:0.001:0.6;

x = 5 * sin(2*pi*50*t)+ 10 * sin(2*pi*200*t);

33

y = x + 2*randn(size(t));

y = y(1:512); y = y + abs(min(y));

y = y / max(y);

y = 1000 * y;

pwelch(y, window(@hamming,512),[],512,1000);

The sampled signal is also given to the Micro-controller and it detects peaks at 50.7813

Hz and 199.2188 Hz. Therefore, the Micro-controller can detect frequencies from a signal

that is corrupted by zero-mean random noise.

In the last example, Berrebi’s data is used to detect the pulsating frequency. By using

Matlab’s PWELCH function on his data, the result is shown in figure 5.3.

Figure 5.3: Welch method’s output for Berrebi’s data (Matlab simulation).

First 512 data out of 9006 is used. Only the integer part of the data is considered. The

Matlab code for this manipulation is as follows:

t = 0:0.001:0.6;

x = 5 * sin(2*pi*50*t)+ 10 * sin(2*pi*200*t);

y = x + 2*randn(size(t));

y = y(1:512); y = y + abs(min(y));

y = y / max(y);

y = 1000 * y;

pwelch(y, window(@hamming,512),[],512,1000);

34 Results

Using those data, the Micro-controller detects peaks at 3.9437 Hz, 8.0751 Hz and

12.0188 Hz. Those are exactly similar with Matlab’s output. It shows a harmonic of

fundamental frequency 4Hz. Therefore, as in Berrebi’s implementation using a PC, a

pulsating flow is detected by the micro-controller.

CHAPTER 6

Future Work

The Inverse Fast Fourier Transform can be implemented to verify the present Fast

Fourier Transform. However, the Company, D-Flow Technology, Sweden who supplies

the flow meters, uses Mitsubishi M16 micro-controller to generate flow velocity data

from ultrasonic flow meter. From this data, pulsating flow is detected. The detection

of installation effect (both static and dynamic) can be implemented in that same micro-

controller already in the flow meter. A kernel can be designed to do both tasks (threads)

i.e. generation of flow velocity data and detection of installation effects, in parallel. It

will be more cost efficient and sophisticated then the present detection using matlab and

a laptop.

Figure 6.1: Future implementation for M-16 based Ultrasonic Flow Measurement.

35

CHAPTER 7

Conclusion

The ATMEL AVR AT90CAN128 can perform the FFT operation. The implemented

algorithm can also support some other 8-bit AVR and ATMEGA16. The detection of

pulsating flow of ultrasonic flow meter is performed accurately and satisfies the main

purpose of this thesis.

In the thesis, Floating point number conversion is implemented. The AVR does not

support 64-bit floating-point number and floating-point arithmetic is slower in AVR.

Therefore, 64-bit floating numbers are converted to 16-bit integers to support the AVR

and to make calculations faster. For computing 512-point FFT, 8-bit AVRs those have

2-cycle multiplier instruction take 371904 clock cycles i.e. about 46.49 milliseconds and

for frequency spectra, those take 155520 clock cycles i.e. about 19.44 milliseconds. It is

quite fast to synchronize with the velocity data of the ultrasonic flow meter.

This implementation enables flow meter and heat meter manufacturers to easily imple-

ment flow pulsation detection in their existing hardware, thereby improving billing and

benefits to district heating suppliers.

37

APPENDIX A

Code - Main function

This code calls main functions for FFT and display the results in Hyper Terminal.

/*------------------------------------------------*/

/* Developed by Shuvra Dev Sarker, 2006-----------*/

/* fftFlowMeter : A test program using flow meter input */

#include <avr/io.h>

#include <avr/pgmspace.h>

#include "fftHeader.h" /* Defs for using Fixed-point FFT module */

#include <inttypes.h>

#include <avr/interrupt.h>

#include <avr/signal.h>

#include <stdlib.h>

#include <stdio.h>

#include <math.h>

#define SYSCLK 8000000

#define sample_freq 96.15

/*------------------------------------------------*/

/* Global variables */

char hyper_input[16]; /* Console input buffer */

int16_t capture[FFT_N] = 512, 256, 128 or 64 sample data that will

be used as input in FFT function;

complex_t bfly_Array[FFT_N]; /* FFT buffer */

uint16_t Fspectra[FFT_N/2]; /* Spectrum output buffer */

/*------------------------------------------------*/

/* Functions */

int max(uint16_t container[],int length);

void detect_freq(uint16_t *signal);

/*:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::*/

/*Just for test output*/

39

40 Appendix A

void USART0_Init (unsigned int baud )

/* Set baud rate */

UBRR0H = (unsigned char) (baud>>8);

UBRR0L = (unsigned char) baud;

/* Set frame format: 8data, no parity & 1 stop bits */

UCSR0C = (0<<UMSEL0) | (0<<UPM0) | (0<<USBS0) | (3<<UCSZ0);

/* Enable receiver and transmitter */

UCSR0B = (1<<RXEN0) | (1<<TXEN0);

void USART1_Init (unsigned int baud )

/* Set baud rate */

UBRR1H = (unsigned char) (baud>>8);

UBRR1L = (unsigned char) baud;

/* Set frame format: 8data, no parity & 1 stop bits */

UCSR1C = (0<<UMSEL1) | (0<<UPM1) | (0<<USBS1) | (3<<UCSZ1);

/* Enable receiver and transmitter */

UCSR1B = (1<<RXEN1) | (1<<TXEN1);

uint8_t USART0_Transmit (char data )

/* Wait for empty transmit buffer */

while ( ! ( UCSR0A & (1<<UDRE0)));

/* Put data into buffer, sends the data */

UDR0 = data;

return 0;

uint8_t USART1_Transmit (char data )

/* Wait for empty transmit buffer */

while ( ! ( UCSR1A & (1<<UDRE1)));

/* Put data into buffer, sends the data */

UDR1 = data;

return 0;

uint8_t USART0_Receive (void )

/* Wait for data to be received */

while ( ! (UCSR0A & (1<<RXC0)));

/* Get and return received data from buffer */

return UDR0;

uint8_t USART1_Receive (void )

/* Wait for data to be received */

while ( ! (UCSR1A & (1<<RXC1)));

/* Get and return received data from buffer */

return UDR1;

int main (void)

char *cp;

uint16_t n, s;

uint16_t t_input,t_execution,t_output;

int i;

DDRB = 0xFF;

USART1_Init(25); //38.4kBaud vid 16mhz

fdevopen(USART1_Transmit, USART1_Receive, 0);

TCCR1B = 3; /* clk/64 */

printf("FFT sample program\r\n");

41

for(;;)

printf("\r\n>");

scanf("%s",hyper_input);

cp = hyper_input;

switch (*cp++) /* Pick a header char (command) */

case ’\0’ : /* Blank line */

break;

case ’w’ : /* w: show flow meter data */

printf("%d\r\n ",FFT_N);

for (n = 0; n < FFT_N; n++)

s = flowInput[n];

printf("%d ",s);

break;

case ’s’ : /* s: show spectrum */

TCNT1 = 0; /* performance counter */

fft_input(flowInput, bfly_Array);

t_input = TCNT1;

printf("Input with Hamming window:");

for(i=0; i<FFT_N; i++)

printf("%d ",bfly_Array[i]);

printf("\r\n\r\n");

TCNT1 = 0;

fft_execute(bfly_Array);

t_execution = TCNT1;

printf("After Exacution of FFT:");

for(i=0; i<FFT_N; i++)

printf("%d ",bfly_Array[i]);

printf("\r\n\r\n");

printf("Fourier spectra:");

TCNT1 = 0;

fft_output(bfly_Array, Fspectra);

t_output = TCNT1;

for(i=0; i<FFT_N/2; i++)

printf("%u ",Fspectra[i]);

detect_freq(Fspectra);

printf("\r\ninput=%u, execute=%u, output=%u (x64clk)", t_input,t_execution,t_output);

break;

default : /* Unknown command */

printf("\n???");

return 0;

void detect_freq(uint16_t signal[])

uint16_t container[3];

42 Appendix A

int i,data,pos,sum, avg_signal;

double freq;



sum = 0;

for(i=0;i< FFT_N/2 ;i++)

sum= sum + signal[i];

avg_signal = ceil((double)sum/(FFT_N/2));

data = 3;

while(data < FFT_N/2 -1)

i = 0; pos = 0;

container[i]= signal[data];

container[i+1]= signal[data+1];

container[i+2]= signal[data+2];

if (avg_signal<container[i] && avg_signal<container[i+1] && avg_signal<container[i+2])

pos = max(container,3);

freq = ((double)(data+pos))*sample_freq/FFT_N;

printf("\r\nFrequency found in: %3.4f Hz",freq);

data = data + 3;

else

data = data + 1;

int max(uint16_t container[],int length)

int max = 0, i, pos = 0;

for(i = 0; i<length;i++)

if(container[i] > max)

max = container[i];

pos = i;

return pos;

APPENDIX B

Code - Macros

The following code represents all macros for FFT in Assembly language. This is the

header file of the fftSource.S, source file.

#ifndef FFT_N

#define FFT_N 512 /* Number of samples (64,128,256,512). */

#ifndef FFFT_ASM /* for c modules */

typedef struct _tag_complex_t

int16_t r;

int16_t i;

complex_t;

#ifndef INPUT_NOUSE

#ifdef INPUT_IQ

void fft_input (const complex_t *, complex_t *);

#else

void fft_input (const int16_t *, complex_t *);

#endif

#endif

void fft_execute (complex_t *);

void fft_output (complex_t *, uint16_t *);

int16_t fmuls_f (int16_t, int16_t);

extern const prog_int16_t tbl_window[];

#else /* for asm module */

#define R0L r0

#define R0H r1

#define R2L r2

#define R2H r3

#define R4L r4

#define R4H r5

#define R6L r6

#define R6H r7

#define R8L r8

#define R8H r9

#define R10L r10

43

44 Appendix B

#define R10H r11

#define R12L r12

#define R12H r13

#define R14L r14

#define R14H r15

#define AL r16

#define AH r17

#define BL r18

#define BH r19

#define CL r20

#define CH r21

#define DL r22

#define DH r23

#define EL r24

#define EH r25

#define XL r26

#define XH r27

#define YL r28

#define YH r29

#define ZL r30

#define ZH r31

.macro ldiw dh,dl, abs

ldi \dl, lo8(\abs)

ldi \dh, hi8(\abs)

.endm

.macro subiw dh,dl, abs

subi \dl, lo8(\abs)

sbci \dh, hi8(\abs)

.endm

.macro addw dh,dl, sh,sl

add \dl, \sl

adc \dh, \sh

.endm

.macro addd d3,d2,d1,d0, s3,s2,s1,s0

add \d0, \s0

adc \d1, \s1

adc \d2, \s2

adc \d3, \s3

.endm

.macro subw dh,dl, sh,sl

sub \dl, \sl

sbc \dh, \sh

.endm

.macro subd d3,d2,d1,d0, s3,s2,s1,s0

sub \d0, \s0

sbc \d1, \s1

sbc \d2, \s2

sbc \d3, \s3

.endm

.macro lddw dh,dl, src

ldd \dl, \src

ldd \dh, \src+1

.endm

.macro ldw dh,dl, src

ld \dl, \src

45

ld \dh, \src

.endm

.macro stw dst, sh,sl

st \dst, \sl

st \dst, \sh

.endm

.macro clrw dh, dl

clr \dh

clr \dl

.endm

.macro lsrw dh, dl

lsr \dh

ror \dl

.endm

.macro asrw dh, dl

asr \dh

ror \dl

.endm

.macro lslw dh, dl

lsl \dl

rol \dh

.endm

.macro pushw dh, dl

push \dh

push \dl

.endm

.macro popw dh, dl

pop \dl

pop \dh

.endm

.macro lpmw dh,dl, src

lpm \dl, \src

lpm \dh, \src

.endm

.macro rjne lbl

breq 99f

rjmp \lbl

99: .endm

// From AVR Data sheet

.macro FMULS16 d3,d2,d1,d0 ,s1h,s1l, s2h,s2l ;Fractional Multiply

(19clk)

fmuls \s1h, \s2h

movw \d2, R0L

fmul \s1l, \s2l

movw \d0, R0L

adc \d2, EH ;EH: zero reg.

fmulsu \s1h, \s2l

sbc \d3, EH

add \d1, R0L

adc \d2, R0H

adc \d3, EH

fmulsu \s2h, \s1l

46 Appendix B

sbc \d3, EH

add \d1, R0L

adc \d2, R0H

adc \d3, EH

.endm

.macro SQRT32 ; 32bit square root (526..542clk)

clr R6L

clr R6H

clr R8L

clr R8H

ldi BL, 1

ldi BH, 0

clr CL

clr CH

ldi DH, 16

90: lsl R2L

rol R2H

rol R4L

rol R4H

rol R6L

rol R6H

rol R8L

rol R8H

lsl R2L

rol R2H

rol R4L

rol R4H

rol R6L

rol R6H

rol R8L

rol R8H

brpl 91f

add R6L, BL

adc R6H, BH

adc R8L, CL

adc R8H, CH

rjmp 92f

91: sub R6L, BL

sbc R6H, BH

sbc R8L, CL

sbc R8H, CH

92: lsl BL

rol BH

rol CL

andi BL, 0b11111000

ori BL, 0b00000101

sbrc R8H, 7

subi BL, 2

dec DH

brne 90b

lsr CL

ror BH

ror BL

lsr CL

ror BH

ror BL

.endm

#endif /* FFFT_ASM */

#endif /* FFT_N */

APPENDIX C

Code - Function Descriptionand constant tables

The following code executes the fft input(), fft execute, fft output functions and the

constant tables.

; void fft_input (const int16_t *flowInput, complex_t *bfly_Array);

; void fft_execute (complex_t *bfly_Array);

; void fft_output (complex_t *bfly_Array, uint16_t *Fspectra);

;

; <flowInput>: flow meter input to be processed.

; <bfly_Array>: Complex array for butterfly operations.

; <Fspectra>: Spectrum output buffer.

;

; These functions must be called in sequence to do a DFT in FFT algorithm.

; fft_input() fills the complex array with the flow meter data to prepare butterfly

; operations. A hamming window is applied at the same time.

; fft_execute() executes the butterfly operations.

; fft_output() re-orders the results, converts the complex spectrum into

; scalar spectrum and output it in linear scale.

;

; The number of points FFT_N is defined in "fftHeader.h" and the value can be 64,

; 128, 256 or 512.

;

.nolist

#define FFFT_ASM

#include "fftHeader.h"

.list

#if FFT_N == 512

#define FFT_B 9

#elif FFT_N == 256

#define FFT_B 8

#elif FFT_N == 128

#define FFT_B 7

#elif FFT_N == 64

#define FFT_B 6

#else

47

48 Appendix C

#error FFT_N must be 64,128,256 or 512.

#endif

;----------------------------------------------------------------------------;

; Constant Tables

.global tbl_window

tbl_window: ; tbl_window[] = ... (This is a Hamming window)

#if FFT_N == 512

.dc.w 2621, 2622, 2626, 2632, 2640, 2650, 2662, 2677, 2694, 2714, 2735, 2759, 2785, 2814, 2844, 2877

.dc.w 2912, 2949, 2989, 3031, 3075, 3121, 3169, 3220, 3273, 3328, 3385, 3444, 3506, 3569, 3635, 3703

.dc.w 3773, 3845, 3919, 3996, 4074, 4155, 4237, 4321, 4408, 4496, 4587, 4680, 4774, 4870, 4969, 5069

.dc.w 5171, 5275, 5381, 5489, 5599, 5710, 5824, 5939, 6056, 6174, 6295, 6417, 6541, 6666, 6793, 6922

.dc.w 7052, 7185, 7318, 7453, 7590, 7728, 7868, 8010, 8152, 8296, 8442, 8589, 8737, 8887, 9038, 9191

.dc.w 9344, 9499, 9655, 9813, 9971, 10131, 10292, 10454, 10617, 10781, 10946, 11113, 11280, 11448, 11617, 11787

.dc.w 11958, 12130, 12303, 12476, 12650, 12825, 13001, 13178, 13355, 13533, 13711, 13890, 14070, 14250, 14431, 14612

.dc.w 14793, 14975, 15158, 15341, 15524, 15708, 15892, 16076, 16260, 16445, 16629, 16814, 16999, 17185, 17370, 17555

.dc.w 17741, 17926, 18111, 18296, 18481, 18667, 18851, 19036, 19221, 19405, 19589, 19773, 19956, 20139, 20322, 20504

.dc.w 20686, 20867, 21048, 21229, 21409, 21588, 21767, 21945, 22122, 22299, 22475, 22651, 22825, 22999, 23172, 23344

.dc.w 23516, 23686, 23856, 24025, 24192, 24359, 24525, 24689, 24853, 25016, 25177, 25337, 25496, 25654, 25811, 25967

.dc.w 26121, 26274, 26426, 26576, 26725, 26873, 27019, 27164, 27308, 27450, 27590, 27729, 27867, 28003, 28137, 28270

.dc.w 28401, 28531, 28659, 28785, 28910, 29033, 29154, 29274, 29391, 29507, 29622, 29734, 29845, 29953, 30060, 30165

.dc.w 30268, 30370, 30469, 30566, 30662, 30755, 30847, 30936, 31024, 31109, 31193, 31274, 31354, 31431, 31506, 31579

.dc.w 31650, 31719, 31786, 31851, 31913, 31974, 32032, 32088, 32142, 32194, 32243, 32291, 32336, 32379, 32419, 32458

.dc.w 32494, 32528, 32560, 32589, 32617, 32642, 32664, 32685, 32703, 32719, 32733, 32744, 32753, 32760, 32764, 32767

.dc.w 32767, 32764, 32760, 32753, 32744, 32733, 32719, 32703, 32685, 32664, 32642, 32617, 32589, 32560, 32528, 32494

.dc.w 32458, 32419, 32379, 32336, 32291, 32243, 32194, 32142, 32088, 32032, 31974, 31913, 31851, 31786, 31719, 31650

.dc.w 31579, 31506, 31431, 31354, 31274, 31193, 31109, 31024, 30936, 30847, 30755, 30662, 30566, 30469, 30370, 30268

.dc.w 30165, 30060, 29953, 29845, 29734, 29622, 29507, 29391, 29274, 29154, 29033, 28910, 28785, 28659, 28531, 28401

.dc.w 28270, 28137, 28003, 27867, 27729, 27590, 27450, 27308, 27164, 27019, 26873, 26725, 26576, 26426, 26274, 26121

.dc.w 25967, 25811, 25654, 25496, 25337, 25177, 25016, 24853, 24689, 24525, 24359, 24192, 24025, 23856, 23686, 23516

.dc.w 23344, 23172, 22999, 22825, 22651, 22475, 22299, 22122, 21945, 21767, 21588, 21409, 21229, 21048, 20867, 20686

.dc.w 20504, 20322, 20139, 19956, 19773, 19589, 19405, 19221, 19036, 18851, 18667, 18481, 18296, 18111, 17926, 17741

.dc.w 17555, 17370, 17185, 16999, 16814, 16629, 16445, 16260, 16076, 15892, 15708, 15524, 15341, 15158, 14975, 14793

.dc.w 14612, 14431, 14250, 14070, 13890, 13711, 13533, 13355, 13178, 13001, 12825, 12650, 12476, 12303, 12130, 11958

.dc.w 11787, 11617, 11448, 11280, 11113, 10946, 10781, 10617, 10454, 10292, 10131, 9971, 9813, 9655, 9499, 9344

.dc.w 9191, 9038, 8887, 8737, 8589, 8442, 8296, 8152, 8010, 7868, 7728, 7590, 7453, 7318, 7185, 7052

.dc.w 6922, 6793, 6666, 6541, 6417, 6295, 6174, 6056, 5939, 5824, 5710, 5599, 5489, 5381, 5275, 5171

.dc.w 5069, 4969, 4870, 4774, 4680, 4587, 4496, 4408, 4321, 4237, 4155, 4074, 3996, 3919, 3845, 3773

.dc.w 3703, 3635, 3569, 3506, 3444, 3385, 3328, 3273, 3220, 3169, 3121, 3075, 3031, 2989, 2949, 2912

.dc.w 2877, 2844, 2814, 2785, 2759, 2735, 2714, 2694, 2677, 2662, 2650, 2640, 2632, 2626, 2622, 2621

#elif FFT_N == 256

.dc.w 2621, 2626, 2640, 2663, 2695, 2736, 2786, 2845, 2913, 2990, 3077, 3172, 3275, 3388, 3509, 3639

.dc.w 3778, 3924, 4080, 4243, 4415, 4595, 4782, 4978, 5181, 5392, 5610, 5836, 6069, 6308, 6555, 6809

.dc.w 7069, 7336, 7608, 7888, 8173, 8463, 8760, 9061, 9368, 9681, 9998, 10319, 10645, 10976, 11310, 11648

.dc.w 11990, 12336, 12685, 13036, 13391, 13748, 14108, 14470, 14833, 15199, 15566, 15934, 16303, 16674, 17044, 17416

.dc.w 17787, 18158, 18529, 18900, 19270, 19639, 20006, 20372, 20737, 21100, 21461, 21819, 22175, 22528, 22878, 23226

.dc.w 23569, 23910, 24246, 24578, 24907, 25231, 25550, 25864, 26174, 26478, 26778, 27071, 27359, 27641, 27917, 28187

.dc.w 28450, 28707, 28957, 29201, 29437, 29666, 29888, 30103, 30310, 30509, 30701, 30885, 31060, 31228, 31387, 31538

.dc.w 31681, 31815, 31941, 32058, 32166, 32265, 32356, 32438, 32510, 32574, 32629, 32674, 32711, 32738, 32757, 32766

.dc.w 32766, 32757, 32738, 32711, 32674, 32629, 32574, 32510, 32438, 32356, 32265, 32166, 32058, 31941, 31815, 31681

.dc.w 31538, 31387, 31228, 31060, 30885, 30701, 30509, 30310, 30103, 29888, 29666, 29437, 29201, 28957, 28707, 28450

.dc.w 28187, 27917, 27641, 27359, 27071, 26778, 26478, 26174, 25864, 25550, 25231, 24907, 24578, 24246, 23910, 23569

.dc.w 23226, 22878, 22528, 22175, 21819, 21461, 21100, 20737, 20372, 20006, 19639, 19270, 18900, 18529, 18158, 17787

.dc.w 17416, 17044, 16674, 16303, 15934, 15566, 15199, 14833, 14470, 14108, 13748, 13391, 13036, 12685, 12336, 11990

.dc.w 11648, 11310, 10976, 10645, 10319, 9998, 9681, 9368, 9061, 8760, 8463, 8173, 7888, 7608, 7336, 7069

.dc.w 6809, 6555, 6308, 6069, 5836, 5610, 5392, 5181, 4978, 4782, 4595, 4415, 4243, 4080, 3924, 3778

.dc.w 3639, 3509, 3388, 3275, 3172, 3077, 2990, 2913, 2845, 2786, 2736, 2695, 2663, 2640, 2626, 2621

#elif FFT_N == 128

.dc.w 2621, 2640, 2695, 2787, 2916, 3080, 3281, 3516, 3787, 4091, 4429, 4799, 5201, 5633, 6095, 6585

.dc.w 7102, 7645, 8213, 8804, 9417, 10050, 10702, 11371, 12055, 12754, 13464, 14185, 14914, 15650, 16391, 17135

.dc.w 17881, 18626, 19369, 20107, 20840, 21565, 22281, 22985, 23677, 24354, 25014, 25657, 26280, 26882, 27462, 28018

.dc.w 28548, 29052, 29528, 29975, 30393, 30779, 31133, 31454, 31741, 31994, 32212, 32395, 32542, 32652, 32726, 32762

.dc.w 32762, 32726, 32652, 32542, 32395, 32212, 31994, 31741, 31454, 31133, 30779, 30393, 29975, 29528, 29052, 28548

.dc.w 28018, 27462, 26882, 26280, 25657, 25014, 24354, 23677, 22985, 22281, 21565, 20840, 20107, 19369, 18626, 17881

.dc.w 17135, 16391, 15650, 14914, 14185, 13464, 12754, 12055, 11371, 10702, 10050, 9417, 8804, 8213, 7645, 7102

.dc.w 6585, 6095, 5633, 5201, 4799, 4429, 4091, 3787, 3516, 3281, 3080, 2916, 2787, 2695, 2640, 2621

#elif FFT_N == 64

.dc.w 2621, 2696, 2920, 3291, 3805, 4457, 5240, 6148, 7170, 8296, 9516, 10818, 12187, 13612, 15077, 16568

.dc.w 18070, 19568, 21048, 22495, 23893, 25231, 26493, 27668, 28743, 29709, 30556, 31274, 31858, 32301, 32599, 32748

.dc.w 32748, 32599, 32301, 31858, 31274, 30556, 29709, 28743, 27668, 26493, 25231, 23893, 22495, 21048, 19568, 18070

.dc.w 16568, 15077, 13612, 12187, 10818, 9516, 8296, 7170, 6148, 5240, 4457, 3805, 3291, 2920, 2696, 2621

#endif

tbl_cos_sin: ; Table of cos(x),sin(x), (0 <= x < pi, in FFT_N/2 steps)

#if FFT_N == 512

49

.dc.w 32767, 0, 32764, 402, 32757, 804, 32744, 1206, 32727, 1607, 32705, 2009, 32678, 2410, 32646, 2811

.dc.w 32609, 3211, 32567, 3611, 32520, 4011, 32468, 4409, 32412, 4807, 32350, 5205, 32284, 5601, 32213, 5997

.dc.w 32137, 6392, 32056, 6786, 31970, 7179, 31880, 7571, 31785, 7961, 31684, 8351, 31580, 8739, 31470, 9126

.dc.w 31356, 9511, 31236, 9895, 31113, 10278, 30984, 10659, 30851, 11038, 30713, 11416, 30571, 11792, 30424, 12166

.dc.w 30272, 12539, 30116, 12909, 29955, 13278, 29790, 13645, 29621, 14009, 29446, 14372, 29268, 14732, 29085, 15090

.dc.w 28897, 15446, 28706, 15799, 28510, 16150, 28309, 16499, 28105, 16845, 27896, 17189, 27683, 17530, 27466, 17868

.dc.w 27244, 18204, 27019, 18537, 26789, 18867, 26556, 19194, 26318, 19519, 26077, 19840, 25831, 20159, 25582, 20474

.dc.w 25329, 20787, 25072, 21096, 24811, 21402, 24546, 21705, 24278, 22004, 24006, 22301, 23731, 22594, 23452, 22883

.dc.w 23169, 23169, 22883, 23452, 22594, 23731, 22301, 24006, 22004, 24278, 21705, 24546, 21402, 24811, 21096, 25072

.dc.w 20787, 25329, 20474, 25582, 20159, 25831, 19840, 26077, 19519, 26318, 19194, 26556, 18867, 26789, 18537, 27019

.dc.w 18204, 27244, 17868, 27466, 17530, 27683, 17189, 27896, 16845, 28105, 16499, 28309, 16150, 28510, 15799, 28706

.dc.w 15446, 28897, 15090, 29085, 14732, 29268, 14372, 29446, 14009, 29621, 13645, 29790, 13278, 29955, 12909, 30116

.dc.w 12539, 30272, 12166, 30424, 11792, 30571, 11416, 30713, 11038, 30851, 10659, 30984, 10278, 31113, 9895, 31236

.dc.w 9511, 31356, 9126, 31470, 8739, 31580, 8351, 31684, 7961, 31785, 7571, 31880, 7179, 31970, 6786, 32056

.dc.w 6392, 32137, 5997, 32213, 5601, 32284, 5205, 32350, 4807, 32412, 4409, 32468, 4011, 32520, 3611, 32567

.dc.w 3211, 32609, 2811, 32646, 2410, 32678, 2009, 32705, 1607, 32727, 1206, 32744, 804, 32757, 402, 32764

.dc.w 0, 32766, -402, 32764, -804, 32757, -1206, 32744, -1607, 32727, -2009, 32705, -2410, 32678, -2811, 32646

.dc.w -3211, 32609, -3611, 32567, -4010, 32520, -4409, 32468, -4807, 32412, -5205, 32350, -5601, 32284, -5997, 32213

.dc.w -6392, 32137, -6786, 32056, -7179, 31970, -7571, 31880, -7961, 31785, -8351, 31684, -8739, 31580, -9126, 31470

.dc.w -9511, 31356, -9895, 31236, -10278, 31113, -10659, 30984, -11038, 30851, -11416, 30713, -11792, 30571, -12166, 30424

.dc.w -12539, 30272, -12909, 30116, -13278, 29955, -13645, 29790, -14009, 29621, -14372, 29446, -14732, 29268, -15090, 29085

.dc.w -15446, 28897, -15799, 28706, -16150, 28510, -16499, 28309, -16845, 28105, -17189, 27896, -17530, 27683, -17868, 27466

.dc.w -18204, 27244, -18537, 27019, -18867, 26789, -19194, 26556, -19519, 26318, -19840, 26077, -20159, 25831, -20474, 25582

.dc.w -20787, 25329, -21096, 25072, -21402, 24811, -21705, 24546, -22004, 24278, -22301, 24006, -22594, 23731, -22883, 23452

.dc.w -23169, 23169, -23452, 22883, -23731, 22594, -24006, 22301, -24278, 22005, -24546, 21705, -24811, 21402, -25072, 21096

.dc.w -25329, 20787, -25582, 20474, -25831, 20159, -26077, 19840, -26318, 19519, -26556, 19194, -26789, 18867, -27019, 18537

.dc.w -27244, 18204, -27466, 17868, -27683, 17530, -27896, 17189, -28105, 16845, -28309, 16499, -28510, 16150, -28706, 15799

.dc.w -28897, 15446, -29085, 15090, -29268, 14732, -29446, 14372, -29620, 14009, -29790, 13645, -29955, 13278, -30116, 12910

.dc.w -30272, 12539, -30424, 12167, -30571, 11792, -30713, 11416, -30851, 11038, -30984, 10659, -31113, 10278, -31236, 9895

.dc.w -31356, 9511, -31470, 9126, -31580, 8739, -31684, 8351, -31784, 7961, -31880, 7571, -31970, 7179, -32056, 6786

.dc.w -32137, 6392, -32213, 5997, -32284, 5601, -32350, 5205, -32412, 4807, -32468, 4409, -32520, 4011, -32567, 3611

.dc.w -32609, 3211, -32646, 2811, -32678, 2410, -32705, 2009, -32727, 1607, -32744, 1206, -32757, 804, -32764, 402

#elif FFT_N == 256

.dc.w 32767, 0, 32757, 804, 32727, 1607, 32678, 2410, 32609, 3211, 32520, 4011, 32412, 4807, 32284, 5601

.dc.w 32137, 6392, 31970, 7179, 31785, 7961, 31580, 8739, 31356, 9511, 31113, 10278, 30851, 11038, 30571, 11792

.dc.w 30272, 12539, 29955, 13278, 29621, 14009, 29268, 14732, 28897, 15446, 28510, 16150, 28105, 16845, 27683, 17530

.dc.w 27244, 18204, 26789, 18867, 26318, 19519, 25831, 20159, 25329, 20787, 24811, 21402, 24278, 22004, 23731, 22594

.dc.w 23169, 23169, 22594, 23731, 22004, 24278, 21402, 24811, 20787, 25329, 20159, 25831, 19519, 26318, 18867, 26789

.dc.w 18204, 27244, 17530, 27683, 16845, 28105, 16150, 28510, 15446, 28897, 14732, 29268, 14009, 29621, 13278, 29955

.dc.w 12539, 30272, 11792, 30571, 11038, 30851, 10278, 31113, 9511, 31356, 8739, 31580, 7961, 31785, 7179, 31970

.dc.w 6392, 32137, 5601, 32284, 4807, 32412, 4011, 32520, 3211, 32609, 2410, 32678, 1607, 32727, 804, 32757

.dc.w 0, 32766, -804, 32757, -1607, 32727, -2410, 32678, -3211, 32609, -4010, 32520, -4807, 32412, -5601, 32284

.dc.w -6392, 32137, -7179, 31970, -7961, 31785, -8739, 31580, -9511, 31356, -10278, 31113, -11038, 30851, -11792, 30571

.dc.w -12539, 30272, -13278, 29955, -14009, 29621, -14732, 29268, -15446, 28897, -16150, 28510, -16845, 28105, -17530, 27683

.dc.w -18204, 27244, -18867, 26789, -19519, 26318, -20159, 25831, -20787, 25329, -21402, 24811, -22004, 24278, -22594, 23731

.dc.w -23169, 23169, -23731, 22594, -24278, 22005, -24811, 21402, -25329, 20787, -25831, 20159, -26318, 19519, -26789, 18867

.dc.w -27244, 18204, -27683, 17530, -28105, 16845, -28510, 16150, -28897, 15446, -29268, 14732, -29620, 14009, -29955, 13278

.dc.w -30272, 12539, -30571, 11792, -30851, 11038, -31113, 10278, -31356, 9511, -31580, 8739, -31784, 7961, -31970, 7179

.dc.w -32137, 6392, -32284, 5601, -32412, 4807, -32520, 4011, -32609, 3211, -32678, 2410, -32727, 1607, -32757, 804

#elif FFT_N == 128

.dc.w 32767, 0, 32727, 1607, 32609, 3211, 32412, 4807, 32137, 6392, 31785, 7961, 31356, 9511, 30851, 11038

.dc.w 30272, 12539, 29621, 14009, 28897, 15446, 28105, 16845, 27244, 18204, 26318, 19519, 25329, 20787, 24278, 22004

.dc.w 23169, 23169, 22004, 24278, 20787, 25329, 19519, 26318, 18204, 27244, 16845, 28105, 15446, 28897, 14009, 29621

.dc.w 12539, 30272, 11038, 30851, 9511, 31356, 7961, 31785, 6392, 32137, 4807, 32412, 3211, 32609, 1607, 32727

.dc.w 0, 32766, -1607, 32727, -3211, 32609, -4807, 32412, -6392, 32137, -7961, 31785, -9511, 31356, -11038, 30851

.dc.w -12539, 30272, -14009, 29621, -15446, 28897, -16845, 28105, -18204, 27244, -19519, 26318, -20787, 25329, -22004, 24278

.dc.w -23169, 23169, -24278, 22005, -25329, 20787, -26318, 19519, -27244, 18204, -28105, 16845, -28897, 15446, -29620, 14009

.dc.w -30272, 12539, -30851, 11038, -31356, 9511, -31784, 7961, -32137, 6392, -32412, 4807, -32609, 3211, -32727, 1607

#elif FFT_N == 64

.dc.w 32767, 0, 32609, 3211, 32137, 6392, 31356, 9511, 30272, 12539, 28897, 15446, 27244, 18204, 25329, 20787

.dc.w 23169, 23169, 20787, 25329, 18204, 27244, 15446, 28897, 12539, 30272, 9511, 31356, 6392, 32137, 3211, 32609

.dc.w 0, 32766, -3211, 32609, -6392, 32137, -9511, 31356, -12539, 30272, -15446, 28897, -18204, 27244, -20787, 25329

.dc.w -23169, 23169, -25329, 20787, -27244, 18204, -28897, 15446, -30272, 12539, -31356, 9511, -32137, 6392, -32609, 3211

#endif

tbl_bitrev: ; tbl_bitrev[] = ...

#if FFT_N == 512

#ifdef INPUT_IQ

.dc.w 1*4, 257*4, 129*4, 385*4, 65*4, 321*4, 193*4, 449*4, 33*4, 289*4, 161*4, 417*4, 97*4, 353*4, 225*4, 481*4

.dc.w 17*4, 273*4, 145*4, 401*4, 81*4, 337*4, 209*4, 465*4, 49*4, 305*4, 177*4, 433*4, 113*4, 369*4, 241*4, 497*4

.dc.w 9*4, 265*4, 137*4, 393*4, 73*4, 329*4, 201*4, 457*4, 41*4, 297*4, 169*4, 425*4, 105*4, 361*4, 233*4, 489*4

.dc.w 25*4, 281*4, 153*4, 409*4, 89*4, 345*4, 217*4, 473*4, 57*4, 313*4, 185*4, 441*4, 121*4, 377*4, 249*4, 505*4

.dc.w 5*4, 261*4, 133*4, 389*4, 69*4, 325*4, 197*4, 453*4, 37*4, 293*4, 165*4, 421*4, 101*4, 357*4, 229*4, 485*4

.dc.w 21*4, 277*4, 149*4, 405*4, 85*4, 341*4, 213*4, 469*4, 53*4, 309*4, 181*4, 437*4, 117*4, 373*4, 245*4, 501*4

.dc.w 13*4, 269*4, 141*4, 397*4, 77*4, 333*4, 205*4, 461*4, 45*4, 301*4, 173*4, 429*4, 109*4, 365*4, 237*4, 493*4

.dc.w 29*4, 285*4, 157*4, 413*4, 93*4, 349*4, 221*4, 477*4, 61*4, 317*4, 189*4, 445*4, 125*4, 381*4, 253*4, 509*4

.dc.w 3*4, 259*4, 131*4, 387*4, 67*4, 323*4, 195*4, 451*4, 35*4, 291*4, 163*4, 419*4, 99*4, 355*4, 227*4, 483*4

.dc.w 19*4, 275*4, 147*4, 403*4, 83*4, 339*4, 211*4, 467*4, 51*4, 307*4, 179*4, 435*4, 115*4, 371*4, 243*4, 499*4

.dc.w 11*4, 267*4, 139*4, 395*4, 75*4, 331*4, 203*4, 459*4, 43*4, 299*4, 171*4, 427*4, 107*4, 363*4, 235*4, 491*4

50 Appendix C

.dc.w 27*4, 283*4, 155*4, 411*4, 91*4, 347*4, 219*4, 475*4, 59*4, 315*4, 187*4, 443*4, 123*4, 379*4, 251*4, 507*4

.dc.w 7*4, 263*4, 135*4, 391*4, 71*4, 327*4, 199*4, 455*4, 39*4, 295*4, 167*4, 423*4, 103*4, 359*4, 231*4, 487*4

.dc.w 23*4, 279*4, 151*4, 407*4, 87*4, 343*4, 215*4, 471*4, 55*4, 311*4, 183*4, 439*4, 119*4, 375*4, 247*4, 503*4

.dc.w 15*4, 271*4, 143*4, 399*4, 79*4, 335*4, 207*4, 463*4, 47*4, 303*4, 175*4, 431*4, 111*4, 367*4, 239*4, 495*4

.dc.w 31*4, 287*4, 159*4, 415*4, 95*4, 351*4, 223*4, 479*4, 63*4, 319*4, 191*4, 447*4, 127*4, 383*4, 255*4, 511*4

#endif

.dc.w 0*4, 256*4, 128*4, 384*4, 64*4, 320*4, 192*4, 448*4, 32*4, 288*4, 160*4, 416*4, 96*4, 352*4, 224*4, 480*4

.dc.w 16*4, 272*4, 144*4, 400*4, 80*4, 336*4, 208*4, 464*4, 48*4, 304*4, 176*4, 432*4, 112*4, 368*4, 240*4, 496*4

.dc.w 8*4, 264*4, 136*4, 392*4, 72*4, 328*4, 200*4, 456*4, 40*4, 296*4, 168*4, 424*4, 104*4, 360*4, 232*4, 488*4

.dc.w 24*4, 280*4, 152*4, 408*4, 88*4, 344*4, 216*4, 472*4, 56*4, 312*4, 184*4, 440*4, 120*4, 376*4, 248*4, 504*4

.dc.w 4*4, 260*4, 132*4, 388*4, 68*4, 324*4, 196*4, 452*4, 36*4, 292*4, 164*4, 420*4, 100*4, 356*4, 228*4, 484*4

.dc.w 20*4, 276*4, 148*4, 404*4, 84*4, 340*4, 212*4, 468*4, 52*4, 308*4, 180*4, 436*4, 116*4, 372*4, 244*4, 500*4

.dc.w 12*4, 268*4, 140*4, 396*4, 76*4, 332*4, 204*4, 460*4, 44*4, 300*4, 172*4, 428*4, 108*4, 364*4, 236*4, 492*4

.dc.w 28*4, 284*4, 156*4, 412*4, 92*4, 348*4, 220*4, 476*4, 60*4, 316*4, 188*4, 444*4, 124*4, 380*4, 252*4, 508*4

.dc.w 2*4, 258*4, 130*4, 386*4, 66*4, 322*4, 194*4, 450*4, 34*4, 290*4, 162*4, 418*4, 98*4, 354*4, 226*4, 482*4

.dc.w 18*4, 274*4, 146*4, 402*4, 82*4, 338*4, 210*4, 466*4, 50*4, 306*4, 178*4, 434*4, 114*4, 370*4, 242*4, 498*4

.dc.w 10*4, 266*4, 138*4, 394*4, 74*4, 330*4, 202*4, 458*4, 42*4, 298*4, 170*4, 426*4, 106*4, 362*4, 234*4, 490*4

.dc.w 26*4, 282*4, 154*4, 410*4, 90*4, 346*4, 218*4, 474*4, 58*4, 314*4, 186*4, 442*4, 122*4, 378*4, 250*4, 506*4

.dc.w 6*4, 262*4, 134*4, 390*4, 70*4, 326*4, 198*4, 454*4, 38*4, 294*4, 166*4, 422*4, 102*4, 358*4, 230*4, 486*4

.dc.w 22*4, 278*4, 150*4, 406*4, 86*4, 342*4, 214*4, 470*4, 54*4, 310*4, 182*4, 438*4, 118*4, 374*4, 246*4, 502*4

.dc.w 14*4, 270*4, 142*4, 398*4, 78*4, 334*4, 206*4, 462*4, 46*4, 302*4, 174*4, 430*4, 110*4, 366*4, 238*4, 494*4

.dc.w 30*4, 286*4, 158*4, 414*4, 94*4, 350*4, 222*4, 478*4, 62*4, 318*4, 190*4, 446*4, 126*4, 382*4, 254*4, 510*4

#elif FFT_N == 256

#ifdef INPUT_IQ

.dc.w 1*4, 129*4, 65*4, 193*4, 33*4, 161*4, 97*4, 225*4, 17*4, 145*4, 81*4, 209*4, 49*4, 177*4, 113*4, 241*4

.dc.w 9*4, 137*4, 73*4, 201*4, 41*4, 169*4, 105*4, 233*4, 25*4, 153*4, 89*4, 217*4, 57*4, 185*4, 121*4, 249*4

.dc.w 5*4, 133*4, 69*4, 197*4, 37*4, 165*4, 101*4, 229*4, 21*4, 149*4, 85*4, 213*4, 53*4, 181*4, 117*4, 245*4

.dc.w 13*4, 141*4, 77*4, 205*4, 45*4, 173*4, 109*4, 237*4, 29*4, 157*4, 93*4, 221*4, 61*4, 189*4, 125*4, 253*4

.dc.w 3*4, 131*4, 67*4, 195*4, 35*4, 163*4, 99*4, 227*4, 19*4, 147*4, 83*4, 211*4, 51*4, 179*4, 115*4, 243*4

.dc.w 11*4, 139*4, 75*4, 203*4, 43*4, 171*4, 107*4, 235*4, 27*4, 155*4, 91*4, 219*4, 59*4, 187*4, 123*4, 251*4

.dc.w 7*4, 135*4, 71*4, 199*4, 39*4, 167*4, 103*4, 231*4, 23*4, 151*4, 87*4, 215*4, 55*4, 183*4, 119*4, 247*4

.dc.w 15*4, 143*4, 79*4, 207*4, 47*4, 175*4, 111*4, 239*4, 31*4, 159*4, 95*4, 223*4, 63*4, 191*4, 127*4, 255*4

#endif

.dc.w 0*4, 128*4, 64*4, 192*4, 32*4, 160*4, 96*4, 224*4, 16*4, 144*4, 80*4, 208*4, 48*4, 176*4, 112*4, 240*4

.dc.w 8*4, 136*4, 72*4, 200*4, 40*4, 168*4, 104*4, 232*4, 24*4, 152*4, 88*4, 216*4, 56*4, 184*4, 120*4, 248*4

.dc.w 4*4, 132*4, 68*4, 196*4, 36*4, 164*4, 100*4, 228*4, 20*4, 148*4, 84*4, 212*4, 52*4, 180*4, 116*4, 244*4

.dc.w 12*4, 140*4, 76*4, 204*4, 44*4, 172*4, 108*4, 236*4, 28*4, 156*4, 92*4, 220*4, 60*4, 188*4, 124*4, 252*4

.dc.w 2*4, 130*4, 66*4, 194*4, 34*4, 162*4, 98*4, 226*4, 18*4, 146*4, 82*4, 210*4, 50*4, 178*4, 114*4, 242*4

.dc.w 10*4, 138*4, 74*4, 202*4, 42*4, 170*4, 106*4, 234*4, 26*4, 154*4, 90*4, 218*4, 58*4, 186*4, 122*4, 250*4

.dc.w 6*4, 134*4, 70*4, 198*4, 38*4, 166*4, 102*4, 230*4, 22*4, 150*4, 86*4, 214*4, 54*4, 182*4, 118*4, 246*4

.dc.w 14*4, 142*4, 78*4, 206*4, 46*4, 174*4, 110*4, 238*4, 30*4, 158*4, 94*4, 222*4, 62*4, 190*4, 126*4, 254*4

#elif FFT_N == 128

#ifdef INPUT_IQ

.dc.w 1*4, 65*4, 33*4, 97*4, 17*4, 81*4, 49*4, 113*4, 9*4, 73*4, 41*4, 105*4, 25*4, 89*4, 57*4, 121*4

.dc.w 5*4, 69*4, 37*4, 101*4, 21*4, 85*4, 53*4, 117*4, 13*4, 77*4, 45*4, 109*4, 29*4, 93*4, 61*4, 125*4

.dc.w 3*4, 67*4, 35*4, 99*4, 19*4, 83*4, 51*4, 115*4, 11*4, 75*4, 43*4, 107*4, 27*4, 91*4, 59*4, 123*4

.dc.w 7*4, 71*4, 39*4, 103*4, 23*4, 87*4, 55*4, 119*4, 15*4, 79*4, 47*4, 111*4, 31*4, 95*4, 63*4, 127*4

#endif

.dc.w 0*4, 64*4, 32*4, 96*4, 16*4, 80*4, 48*4, 112*4, 8*4, 72*4, 40*4, 104*4, 24*4, 88*4, 56*4, 120*4

.dc.w 4*4, 68*4, 36*4, 100*4, 20*4, 84*4, 52*4, 116*4, 12*4, 76*4, 44*4, 108*4, 28*4, 92*4, 60*4, 124*4

.dc.w 2*4, 66*4, 34*4, 98*4, 18*4, 82*4, 50*4, 114*4, 10*4, 74*4, 42*4, 106*4, 26*4, 90*4, 58*4, 122*4

.dc.w 6*4, 70*4, 38*4, 102*4, 22*4, 86*4, 54*4, 118*4, 14*4, 78*4, 46*4, 110*4, 30*4, 94*4, 62*4, 126*4

#elif FFT_N == 64

#ifdef INPUT_IQ

.dc.w 1*4, 33*4, 17*4, 49*4, 9*4, 41*4, 25*4, 57*4, 5*4, 37*4, 21*4, 53*4, 13*4, 45*4, 29*4, 61*4

.dc.w 3*4, 35*4, 19*4, 51*4, 11*4, 43*4, 27*4, 59*4, 7*4, 39*4, 23*4, 55*4, 15*4, 47*4, 31*4, 63*4

#endif

.dc.w 0*4, 32*4, 16*4, 48*4, 8*4, 40*4, 24*4, 56*4, 4*4, 36*4, 20*4, 52*4, 12*4, 44*4, 28*4, 60*4

.dc.w 2*4, 34*4, 18*4, 50*4, 10*4, 42*4, 26*4, 58*4, 6*4, 38*4, 22*4, 54*4, 14*4, 46*4, 30*4, 62*4

#endif

;----------------------------------------------------------------------------;

#ifndef INPUT_NOUSE

.global fft_input

.func fft_input

fft_input:

pushw R2H,R2L

pushw AH,AL

pushw YH,YL

movw XL, EL ;X = hyper_input;

movw YL, DL ;Y = bfly_Array;

clr EH ;Zero

ldiw ZH,ZL, tbl_window ;Z = &tbl_window[0];

ldiw AH,AL, FFT_N ;A = FFT_N;

51

1: lpmw BH,BL, Z+ ;B = *Z++; (window)

ldw CH,CL, X+ ;C = *X++; (I-axis)

FMULS16 DH,DL,R2H,R2L, BH,BL, CH,CL ;D = B * C;

stw Y+, DH,DL ;*Y++ = D;

#ifdef INPUT_IQ

ldw CH,CL, X+ ;C = *X++; (Q-axis)

FMULS16 DH,DL,R2H,R2L, BH,BL, CH,CL ;D = B * C;

#endif

stw Y+, DH,DL ;*Y++ = D;

subiw AH,AL, 1 ;while(--A)

brne 1b ;/

popw YH,YL

popw AH,AL

popw R2H,R2L

clr r1

ret

.endfunc

#endif /* INPUT_NOUSE */

;----------------------------------------------------------------------------;

.global fft_execute

.func fft_execute

fft_execute:

pushw R2H,R2L

pushw R4H,R4L

pushw R6H,R6L

pushw R8H,R8L

pushw R10H,R10L

pushw R12H,R12L

pushw R14H,R14L

pushw AH,AL

pushw YH,YL

movw ZL, EL ;Z = bfly_Array;

ldiw EH,EL, 1 ;E = 1;

ldiw XH,XL, FFT_N/2 ;X = FFT_N/2;

1: ldi AL, 4 ;T12 = E; (angular speed)

mul EL, AL ;

movw R12L, R0L ;

mul EH, AL ;

add R12H, R0L ;/

movw R14L, EL ;T14 = E;

pushw EH,EL

movw YL, ZL ;Z = &bfly_Array[0];

mul XL, AL ;Y = &bfly_Array[X];

addw YH,YL, R0H,R0L ;

mul XH, AL ;

add YH, R0L ;/

pushw ZH,ZL

2: clrw R10H,R10L ;T10 = 0 (angle)

clr EH ;Zero reg.

3: lddw AH,AL, Z+0 ;A = *Z - *Y; *Z++ += *Y;

asrw AH,AL ;

lddw DH,DL, Y+0 ;

asrw DH,DL ;

movw CL, AL ;

subw AH,AL, DH,DL ;

addw CH,CL, DH,DL ;

stw Z+, CH,CL ;/

lddw BH,BL, Z+0 ;B = *Z - *Y; *Z++ += *Y;

asrw BH,BL ;

52 Appendix C

lddw DH,DL, Y+2 ;

asrw DH,DL ;

movw CL, BL ;

subw BH,BL, DH,DL ;

addw CH,CL, DH,DL ;

stw Z+, CH,CL ;/

movw R0L, ZL

ldiw ZH,ZL, tbl_cos_sin ;C = cos(T10); D = sin(T10);

addw ZH,ZL, R10H,R10L ;

lpmw CH,CL, Z+ ;

lpmw DH,DL, Z+ ;/

movw ZL, R0L

FMULS16 R4H,R4L,R2H,R2L, AH,AL, CH,CL ;*Y++ = A * C + B * D;

FMULS16 R8H,R8L,R6H,R6L, BH,BL, DH,DL ;

addd R4H,R4L,R2H,R2L, R8H,R8L,R6H,R6L;

stw Y+, R4H,R4L ;/

FMULS16 R4H,R4L,R2H,R2L, BH,BL, CH,CL ;*Y++ = B * C - A * D;

FMULS16 R8H,R8L,R6H,R6L, AH,AL, DH,DL ;

subd R4H,R4L,R2H,R2L, R8H,R8L,R6H,R6L;

stw Y+, R4H,R4L ;/

addw R10H,R10L, R12H,R12L ;T10 += T12; (next angle)

#if FFT_N >= 128

sbrs R10H, FFT_B - 7 ;while(T10 < pi)

#else

sbrs R10L, FFT_B + 1

#endif

rjmp 3b ;/

ldi AL, 4 ;Y += X; Z += X; (skip split segment)

mul XL, AL

addw YH,YL, R0H,R0L ;

addw ZH,ZL, R0H,R0L ;

mul XH, AL ;

add YH, R0L ;

add ZH, R0L ;/

ldi EL, 1 ;while(--T14)

subw R14H,R14L, EH,EL ;

rjne 2b ;/

popw ZH,ZL

popw EH,EL

lslw EH,EL ;E *= 2;

lsrw XH,XL ;while(X /= 2)

adiw XL, 0 ;

rjne 1b ;/

popw YH,YL

popw AH,AL

popw R14H,R14L

popw R12H,R12L

popw R10H,R10L

popw R8H,R8L

popw R6H,R6L

popw R4H,R4L

popw R2H,R2L

; clr r1

ret

.endfunc

;----------------------------------------------------------------------------;

.global fft_output

.func fft_output

fft_output:

pushw R2H,R2L

pushw R4H,R4L

53

pushw R6H,R6L

pushw R8H,R8L

pushw R10H,R10L

pushw AH,AL

pushw YH,YL

movw R10L, EL ;T10 = bfly_Array;

movw YL, DL ;Y = array_output;

ldiw ZH,ZL, tbl_bitrev ;Z = tbl_bitrev;

clr EH ;Zero

#ifdef INPUT_IQ

ldiw AH,AL, FFT_N ;A = FFT_N; (pluse/minus)

#else

ldiw AH,AL, FFT_N / 2 ;A = FFT_N / 2; (pluse only)

#endif

1: lpmw XH,XL, Z+ ;X = *Z++;

addw XH,XL, R10H,R10L ;X += bfly_Array;

ldw BH,BL, X+ ;B = *X++;

ldw CH,CL, X+ ;C = *X++;

FMULS16 R4H,R4L,R2H,R2L, BH,BL, BH,BL ;T4:T2 = B * B;

FMULS16 R8H,R8L,R6H,R6L, CH,CL, CH,CL ;T8:T6 = C * C;

addd R4H,R4L,R2H,R2L, R8H,R8L,R6H,R6L;T4:T2 += T8:T6;

SQRT32 ;B = sqrt(T4:T2);

stw Y+, BH,BL ;*Y++ = B;

subiw AH,AL, 1 ;while(--A)

rjne 1b ;/

popw YH,YL

popw AH,AL

popw R10H,R10L

popw R8H,R8L

popw R6H,R6L

popw R4H,R4L

popw R2H,R2L

clr r1

ret

.endfunc

;----------------------------------------------------------------------------;

.global fmuls_f

.func fmuls_f

fmuls_f:

movw CL, EL ;C = E;

clr EH ;Zero

FMULS16 ZH,ZL,XH,XL, CH,CL, DH,DL ;Z:X = C * D;

movw EL, ZL

clr r1

ret

.endfunc

APPENDIX D

Code - Flow Meter datafiltering

The following program filters the ultrasonic flow meter data and gets velocity data.

#include <stdio.h>




unsigned char signal_array[11];

int main(void)

int8_t index = 10, flag = 0, i;

uint8_t c = ’\r’, old_c;



printf("\r\ntest:");

while (1)

old_c = c;

c = getchar();

if(flag == 1)

if((old_c == ’10’) && (c==’10’))// Check the 10 & 10 in string

else if(index >=0)

signal_array[index]=c;

index--;

if((old_c == ’10’) && (c==’2’)) // Check the start point of the string

flag = 1;

index = 10;

55

56 Appendix D

if((old_c == ’10’) && (c==’3’)) // Check the end point of the string

flag = 0;

break;

for(i = 0; i<11;i++)

printf("%c ",signal_array[i]);

return 0;

APPENDIX E

Code - Covert float64 tofloat32

The following program converts 64-bit floating-point number to 32-bit floating-point

number.

#include <stdio.h>




#include <stdlib.h>

#include <string.h>

int main(void)

unsigned char ch[8] = 0x40,0x34,0xA0,0x00,0x00,0x00,0x00,0x00;

long lvalue;

double value;

long fraction= (((uint32_t)(ch[1] & 0x0f))<< 19)|

(((uint32_t)(ch[2] & 0xff))<<11)|

(((uint32_t)(ch[3] & 0xff))<<3)|

(((uint32_t)(ch[4]& 0xe0))>>5);

long mantissa=(((uint32_t)(ch[0] & 0x7f))<< 4) |((uint32_t)(ch[1] >> 4));

mantissa = mantissa - 1023 + 127;

lvalue = (((uint32_t)(ch[0] & 0x80)) << 24) | ((0xff & mantissa) << 23) | ((fraction & 0x007fffff));

memcpy(&value,&lvalue,4);



printf("Mantissa: %li\n\r", mantissa);

printf("fraction: %lx\n\r", fraction);

printf("value: %lx\n\r", value);

printf("\r\ntest:");

57

58

printf("%lf %lf", lvalue, value);

return 0;

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detection of flow pulsation by micro-controller equipped

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