design filter

8/3/2019 Design Filter

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Session 6 : Digital Filter Design

The Digital Filter Design

Ir. Dadang Gunawan, Ph.D

Electrical Engineering

University of Indonesia


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The Outline

6.1 State-of-the-art

6.2 The advantages of Digital Filter

6.3 The disadvantages of Digital Filter

6.4 Types of Digital Filter

6.5 How to choose the two types ?

6.6 Example of IIR Filter6.7 Example of FIR Filter

6.8 The three filter

( contd )


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The Outline

6.9 Filter Design Steps

6.9.1 Step 1 : Specification of the filter requirements

6.9.2 Step 2 : Calculation of the filter coefficients

6.9.3 Step 3 : Representation filter by suitable structure

6.9.4 Step 4 : Analysis of Finite Wordlength effects

6.9.5 Step 5 : Implementation of the filter6.10 Review


4/27Session 6 : Digital Filter Design

State of the art

The Digital Filter is one of the key of DSP

A filter is essentially a system or network that

selectively changes the wave shape, amplitude-frequency and/or phase-frequency characteristic of asignal in a desired manner

A filter is purely mathematical algorithm implementedin hardware/software

6.1



State of the art (contd)

The objectives of filter are to improve the quality of asignal (for example, to remove or reduce noise)

Digital filters often operate on digitized analog signals orjust numbers, representing some variable, stored in a

computer memory

Figure 6.1 below represent a simplified block diagram of

a real-time digital filter

6.1



Block Diagram of a-real time digital filter with

analog input and output signals

6.1

Inputfilter

Digitalprocessor

B-bit ADC

with sample

and hold

B-bitDAC

Outputfilter

y(n)x(n)

Figure 6.1



The advantages of digital filter Can have characteristic which are not possible with

analog filters, such as a truly linear phase response It doesnt vary with environmental changes such as

thermal variations, so that it eliminates the need to

calibrate periodically

It can be used at very low frequencies, found in manybiomedical applications

etc.

Find others by yourself

6.2


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The disadvantages of digital filter

SPEED LIMITATION

LONG DESIGN and DEVELOPMENT TIMES

FINITE WORDLENGTH EFFECTS

6.3


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Types of digital filters

=

=1

0

)()()(N

k

knxkhny

INFINITE IMPULSE

RESPONSE( I I R )

FINITE IMPULSE

RESPONSE( F I R )

=

=0

)()()(k

knxkhny

Find out the different !

6.4


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How to choose the two types ?

Choose I I R when the only requirementsare sharp cutoff filters and high throughput.

It will give fewer coefficients than FIR

Choose F I R when the the number of filterCoefficients is not too large and when no

phase distortion is desired

WHY ?

WHY ?

6.5


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Example of IIR filter

Suppose we have one transfer function like this :

For drawing its block diagram, we have to make the

corresponding difference equations :

2

2

1

1

2

2

1

10

1

)(

++=

zaza

zbzbbzH

)2()1()()(

)2()1()()(

210

21

++=

=

nwbnwbnwbny

nwanwanxnw

Watch the

mark+ and -

6.6


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Example of IIR filter (contd)

The block diagram (basic lattice structure) for its IIRfilter is :

6.6

Figure 6.2

6 7


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Example of FIR filter

Suppose we have a transfer function like this :

For drawing its block diagram, we have to make the

corresponding difference equations :

=

=

11

0

1)()(

k

zkhzH

=

=11

0

)()()(k

knxkhny

6.7

6 7


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Example of FIR filter (contd)

The block diagram (basic lattice structure) for its FIR

filter is :

6.7

Figure 6.3

6 7


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From two block diagram above, we can summarize the

computational and storage requirement for both filters :

Example of FIR filter (contd)

I I R F I R

Number of multiplications 5 12Number of additions 4 11

Storage locations (coefficients 8 24

and data )

Discuss the difference

6.7

6 8


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The three filter

LOW PASSfilter : reject the high frequency

BAND PASSfilter : reject any frequency

and pass any frequency

HIGH PASSfilter : reject the low frequency

6.8

6 9


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Filter Design Steps

SPECIFY THE FILTER REQUIREMENTS

CALCULATE THE FILTER COEFFICIENT

REPRESENT FILTER BY A SUITABLE STRUCTURE

ANALYSIS of FINITE WORDLENGTH EFFECTS

IMPELEMENT FILTER IN SOFT/HARDWARE

6.9

6 9 1


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Step 1 : Specification of the filter

requirements

There are 6 key parameters of interest :

p passband deviation

s stopband deviation

fp passband edge frequency

fs stopband edge frequencyAs stopband attenuation = - 20.log10 sAp passband ripple = - 20.log10 (1+p)

6.9.1

6 9 1


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requirements (contd)

Here are the position of each parameter in a lowpassfilter :

6.9.1

Figure 6.4

6 9 1


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This an example of FIRbandpass filter that is designed

to the following requirements :

- passband : 1.8 3.3 kHz

- stopband : 0 - 1.4 kHz and 3.7 5 kHz

- stopband deviation : 0.001

- passband deviation : 0.05- stopband attenuation : - 20.log10 (0.001) = 60 dB

- passband ripple : - 20.log10

(1+0.05) = 0.42 dB

6.9.1

6 9 1


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According to the value of those requirements, here are

the scheme :

6.9.1

Figure 6.5

6 9 2


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Step 2 : Calculation of the filter coefficients

There are several method to calculate it : Impulse invariant ( IIR )

Bilinear Transformation ( IIR )

Pole-zero placement ( IIR )

Window ( FIR )

Frequency Sampling ( FIR )

Optimal ( FIR )

FREE

YOUR

MIND !

Use

TheCom-

puter

6.9.2

6 9 3


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Step 3 : Representation filter by suitable

structure

There are some realization structure : Transversal (direct) (FIR)

Frequency sampling (FIR)

Fast Convolution (FIR)

Direct form (I I R)

Cascade (I I R)

Parallel (I I R)

6.9.3

6.9.4


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Step 4 : Analysis of finite wordlength effects

The main sources of performance degradation indigital filters are :

Input / Output signal quantization Coefficient quantization

Arithmetic roundoff errors

Overflow

ADC noise

Deviations

in the

frequency

response

instability in

IIR filter

6.9.4

6.9.5


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Step 5 : Implementation of the filter

To implement the filter at least we need : Memory (e.g. ROM) for storing filter coefficients

Memory (e.g. RAM) for storing the present and pastsinputs/outputs

Hardware and software multipliers

Adder or arithmetic logic unit

6.9.5

6.10


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Preparation to Review

END of THIS SESSIONARE YOU READY TO REVIEW ?

Before the review,

you have to consider yourself.

If you feel you dont understand yet..

Please ask .

6.10

6.10


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Review

1. Explain about Band-stop filter.

2. Try to explore about disadvantages of digital filter.

And why it becomes like that ?

3. Compare the advantages and disadvantages betweendigital filter and analog filter.

4. Please explain about the relationship between

Discrete Transformation and Filter Design.

design filter

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