design of frequency demodulator using goertzel...

ISSN: 2278 – 909X

International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)

Volume 6, Issue 7, July 2017

680

All Rights Reserved © 2017 IJARECE

Design of Frequency Demodulator Using

Goertzel Algorithm

Rahul Shetty, Pavanalaxmi

Abstract— Far distance Communication between millions

without a modulation is worthless, and Frequency modulation

has many advantages. Frequency modulation with adequate

data transfer capacity gives favorable position in crossing out

actual happening noise. This project deals with the design of

FM demodulator which includes FFT and Goertzel

Demodulators using Xilinx system generator design. Xilinx

system generator, a tool for Matlab environment plays a big

role in implementing signal processing instead on DSP

processors. This tool gives a programming HDL code and thus

bit stream can be effortlessly produced. In this Thesis, a novel

attempt is made to design reusable Goertzel blocks are

designed for performing FM demodulation and its

performance is evaluated with a typical Goertzel algorithm

based system as well as with a system designed using FFT. The

proposed system is designed using MATLAB Simulink, Xilinx

Block sets and system generator, which enables model-based programming approach.

Index Terms— Communication, Demodulation, FFT,

Goertzel, Processors, Simulation.

I. INTRODUCTION

Demodulators plays an important role in the field of digital

signal processing and communications and hence it is used

in various applications like Biomedical signal processing,

digital spectral analysis for speech recognition, imaging and

pattern recognition as well as signal manipulation using

filters, Data compression, instrumentation, machine

Inspection, terrestrial, axon prediction and multimedia,

wireless communication systems, microwave, satellite,

radio-over-fiber(RoF), distribution antenna and radar

systems, software-defined radio and many more

applications.

Amplitude, Frequency and phase are different kinds of

modulation techniques available in communication systems.

In this research Thesis, we motivated to do on FM

techniques because it has better fidelity and noise immunity

over AM. Slope Detector, Balanced Slope Detector, Foster-

Seeley Phase Discriminator, Ratio Detector are direct

methods and Phase Lock Loop is an indirect method for FM

demodulation. Fast Fourier Transform (FFT) and Goertzel

algorithm is approached in this Thesis for Demodulation of

FM signals.

Modulation is defined as the process by which some

characteristics; usually amplitude, frequency or phase, of a

carrier wave varies in accordance with the instantaneous

value of modulating signal, or Modulation is a process of

superimposing a low frequency signal on a high frequency

carrier signal. The systems used to perform modulation are

called as modulators and are considered as the most vital

block of any communication system. Communication

Systems employing these modulators are extensively used

in a large number of applications such as radar, aerospace,

naval/maritime communication, underwater communication,

mobile communication and many more. Out of all the

modulation techniques, frequency modulation (FM) is

widely used because of its many advantages and its

applications range from FM radio stations, on-board

systems for fighter aircrafts, satellites and many more

applications.

Nowadays, digital signal processing plays a vital role in

many real time applications in our day-to-day life and

frequency demodulation techniques are recognized as basic

elements needed for DSP. This provides a platform to

design an algorithm for digital signal processors (DSPs) and

Field Programmable Gate Arrays (FPGAs) based system

design. The invention of digital signal processors (DSPs)

and Field Programmable Gate Arrays (FPGAs) have

spearheaded way for novel digital signal processing

techniques and algorithms that are extremely used in large

number of applications.

A. Objective

In this paper, a reusable Goertzel blocks are designed for

performing FM demodulation and its performance is

evaluated with a typical Goertzel algorithm based system as

well as with a system designed using FFT. The proposed

system is designed using MATLAB Simulink, Xilinx Block

sets and system generator, which enables model-based

programming approach.

ISSN: 2278 – 909X



681


II. MATHEMATICAL ANALYSIS OF FM

DEMODULATOR

Modem with respect to FM mainly has Transmitter and

Receiver sections used to transmit and receive

modulated signal. Transmitter part mainly has desired

signal generator, Encoder, FM modulator and RF up-

converter. Receiver consists of a FM demodulator, a

decoder and decision logic.

A. Frequency Modulation (FM)

Frequency modulation is one form of modulation

where the instantaneous frequency f i(t) is varied

linearly with the message signal m(t) and is given by

expression

fi t = fc + kfm(t) (1)

where, fc is carrier frequency, k f expressed in hertz's

per volt is frequency sensitivity of the modulator.

Frequency modulation wave form is shown in Fig 1.

Fig. 1. Waveform of FM signal

General form of expression for Modulator wave is

given as s(t)= Ac.cos[θ(t)] where Ac is carrier

amplitude which is maintained constant overall and

θ(t) is the angular argument which is varied

accordingly with the message signal m(t). So θ(t)

value will be 2πfc + 2πkf m t . dtt

0 Hence FM wave in

time domain can be expressed as

s(t)=Ac.cos[2πfc + 2πkf m t . dtt

0] (2)

B. Frequency Demodulation

Frequency demodulation is the reverse process of

modulation which recovers the original modulating

signal from the FM wave as shown in Fig 2, and so

FM receiver must be sensitive to the frequency

variations of the incoming signals. As FM signals can

be wide or narrow band is made insensitive to the

amplitude variations and this is achieved by having

amplifier with a high gain, hence in this way any

amplitude variations can be removed.

Fig. 2. Waveform of FM demodulation signal

C. Classification of FM demodulators:

FM demodulators can be classified into

Direct methods:

1. Frequency discriminators/slope detector

2. Balanced Frequency discriminators/ Balanced

slope detector

3. Zero crossing detectors

Indirect methods:

1. Quadrature Demodulators

2. Phase lock loop (PLL)

Indirect method known as PLL and Quadrature

method is explained and designed here.

D. Properties of FM signal

Narrow band FM (NBFM):

A NBFM is the FM signal with less bandwidth. The

modulation index 'ß' is less as compared to 1 radian,

Wide band FM (WBFM):

The bandwidth of WBFM is much larger and the theoretical

value tends to infinity. If the modulation index ß is larger,

ideally FM wave contains the carrier and an infinite number

of sidebands are located around the carrier.

ISSN: 2278 – 909X



682


E. FFT Based Frequency Demodulation

Fig. 3. Block diagram of FFT based Frequency

demodulator

It is a computationally efficient algorithm for computing a

Discrete Fourier Transform (DFT) of sample sizes that are

positive integer powers of 2. The DFT of a N point

sequence of x(n), indexed by n =0, 1,2…N-1 is given by X

(K) = 𝑥 𝑛 . 𝑊𝑁𝑘𝑛𝑁−1

𝑛=0 ; K = 0, 1 …N- Where

𝑥 𝑛 and X(K) are complex numbers. Assume 𝑥 𝑛 has

input data samples in time domain (n = 0, 1… N-1), N

represents the number of input samples, 𝑊𝑁 represents

twiddle factor is defined by, 𝑊𝑁=𝑒−𝑗2𝜋

𝑁 = cos(2 𝜋/N) –

jsin (2𝜋/N), K denotes Index for a frequency Bin width of a

discrete signals (k =0, 1 … N-1), 𝑋 𝐾 2 =

𝑋𝑘𝑟𝑒 2 + 𝑋𝑘𝐼𝑚 2 , where 𝑋𝑘𝑟𝑒 and 𝑋𝑘𝐼𝑚 are real and

imaginary component of output data stream. Xk_index

marks the index of the output data that can be calculated

using 𝑁 ×fin

fs, where N denotes length of the transformation,

fin is input frequency in Hz and 𝑓𝑠 is sampling frequency in

Hz. Frequency can be estimated using k×fs

N.

DFT (i.e. Discrete Fourier Transform) is one of the primary

tools that are used for the frequency analysis of discrete

time signals and to represent a discrete time sequence in

frequency Domain using its spectrum samples. An N-point

discrete Fourier transform (DFT) performs the conversion of

time domain data into frequency domain data. The DFT pair

equation of N point sequence of x(n) is given by,

X(K)= x n . e−j (2π

N)knN−1

n=0 0 ≤ K ≤ N − 1 (3)

The more common and simplified notation for the DFT

is written as,

X(K)= x n . WNknN−1

n=0 0 ≤ K ≤ N − 1 (4)

Where 𝑊𝑁 represents the twiddle factor,

WN = e−j

2π

N = cos

2π

N – j sin

2π

N and N is number of point

FFT. An important issue with the implementation of the

DFT for an N point sequence is the complex computations

that cause problems for high speed signal processing.

III GOERTZEL ALGORITHM BASED FREQUENCY

DEMODULATION

Goertzel algorithm is a digital signal processing technique

most commonly used for single-tone and dual-tone multi

frequency detection (DTMF) in telecommunication systems.

In this Thesis, a novel attempt is made to use the algorithm

for FM demodulation.

Fig. 4. Block diagram of Goertzel based Frequency

demodulator

Goertzel Algorithm, shortly called GA is a Digital Signal

Processing (DSP‟s) technique, for identifying frequency

components of an input signal. Since it uses second order

IIR filter, GA filter bank is necessary for identification of

every individual frequency components. Single tone

detection, Spectrum analysis, Dual-tone Multi-frequency

(DTMF) for telecommunication systems are the application

areas using Goertzel algorithm. The GA filter‟s transfer

function is written as,

X (K) = 1−𝑊𝑁

𝑘 . 𝑍−1

1−2 Cos 2 𝜋k

N . 𝑍−1 + 𝑍−2

(5)

The respective difference equation of this second order IIR

system is,

Vk (n)= x (n) + A Vk(n − 1)- Vk (n − 2); 0 ≤ k ≤ N (6)

X (k) = Yk n = Vk (n) + WNk . Vk(n − 1) (7)

𝑉𝑘 (1) = 𝑉𝑘 (2) = 0 for each value of K.

The 𝑉𝑘 𝑛 equation is iterated for all input samples until the

last state variable 𝑉𝑘 𝑁 is obtained.

The pre-computed coefficients are,

A = 2cos (2 𝜋 k / N) (8)

k = round (f / fs* N) + 1 (9)

WNk = cos (2 𝜋 k / N) - j sin (2 𝜋 k / N) (10)

Thereafter, 𝑌𝑘 𝑛 only needs to be computed once, when n =

N, where x (n) is current input sample, N represents

ISSN: 2278 – 909X



683


Goertzel Block Size is like the number of points in an

equivalent FFT, k represents frequency index of targeted

frequencies, f is targeted frequencies in Hz and fs is

sampling frequency in Hz. The Magnitude squared is given

as,

|X (K)|2 = |Yk (n) | = 𝑉𝑘2 (N) + 𝑉𝑘

2 (N-1) – 2cos (2 𝜋 k /

N)𝑉𝑘 (𝑁) . 𝑉𝑘 (N-1) (11)

Magnitude of X(K) is needed to decode the detected

frequencies. As N increases, 𝐕𝐤(𝐧 − 𝟏) and 𝐕𝐤(𝐧 − 𝟐)

and |𝐗 (𝐊)|𝟐 increases and also it takes longer time

for detecting the frequencies.

The direct form II realization of Goertzel algorithm to detect

a single tone or frequency is shown in Fig. 3.5

Fig . 5. Direct Form II realization of Goertzel Algorithm

The Goertzel algorithm is more efficient than the Fast

Fourier Transform in computing an N-point DFT if less than

N 𝑙𝑜𝑔2 N DFT coefficients are required. In DTMF

detection, we only need 8 of, for example, 205 DFT

coefficients to detect the first harmonics of the 8 possible

tones, and then apply decision logic to choose the strongest

touch tone. Since DTMF signals do not have second

harmonics, we could compute another 8 DFT coefficients to

compute the second harmonics to detect the presence of

speech.

The Goertzel algorithm computes the kth DFT coefficient of

the input signal x[n] using a second-order filter. The kth

DFT coefficient is produced after the filter has processed N

samples: X [k] =𝑦𝑘 [n]|𝑛=𝑁. The key in an implementation is

to run 𝑣𝑘 [n] for N samples and then evaluate 𝑦𝑘 [n]. The

computation for 𝑣𝑘 [n] takes one add (x[n] - 𝑣𝑘 [n-2]) and

one multiply-accumulate per sample. In DTMF detection,

we are only concerned with the power of the kth coefficient:

𝑦𝑘[n]. 𝑦𝑘𝑘[N]

The value of N must be shorter than the samples in half of a

DTMF signaling interval, N < 400, be large enough for

good frequency resolution (N > 512), and meet the relative

error specification. We used a conventional value of N=

205, because it is roughly half of 400 samples. Decision

logic can be added to give a valid DTMF signal if the same

two DTMF tones are detected in a row to add robustness

against noise.

The variable „k‟ mentioned is computed as

K =round(f/fs*N)+1 (12)

Where „f‟ denotes the input frequency tone to be detected,

„fs‟ denotes the sampling frequency and N denotes the

number of points.

In order to detect eight different frequencies from the

modulator generated with a frequency deviation of 1 KHz,

frequency demodulator is designed using Goertzel algorithm

and the parameters are required to detect those frequencies

are tabulated above as shown in tabulation from 1 KHz to

10 KHz.

The value of frequency index k, cosine term A and

parameter WNk with FFT points N=1024 and sampling

frequency fs = 64kHz for detecting eight different various

tones using Goertzel Algorithm the realization structure of

direct form II given in Fig. 3.5. In FFT based realization,

magnitude X[k] is computed for first sample to number of

FFT points i.e. k=1:N, whereas in Goertzel algorithm based

realization, the magnitude X[k] is computed only once for a

particular value of frequency index „K‟ with the help of

above „k‟ relation.

The block diagram for FM demodulation using Goertzel

Algorithm based realization is shown in Fig. 3.4. The

Goertzel blocks are selected based on the frequency

deviation ∆f of the input FM signal from the modulator

blocks designed. The input to the modulator block is 3-bit

counter signal, based on the counter n-bit signal, i.e.

2𝑛 combination of different frequency range is generated

based on the frequency deviation specified on the ∆f in the

ISSN: 2278 – 909X



684


modulator design. The magnitude X[k] from each Goertzel

block output is computed and the decision logic block

shown in Fig. 3.4 is used to find argmaxkX(k), which is in

turn used to find the frequency of the input FM signal and

the output voltage is generated accordingly. An alternative

architecture to the one shown in Fig. 3.5 is given in Fig. 3.4

wherein the same Goertzel block is reused to detect different

frequencies and it is designed with the motive of reducing

hardware resources on increasing the number of frequencies

to be detected.

A. Applications of FFT Algorithm

Spectrum Analyzer for on-board satellite communication

systems requires FFT to compute frequency spectrum of an

input signals.

A.1 Advantages

It is the faster version of DFT; it can be applied to the

number of samples in the signal is power of two. The

number of complex multiplier is greatly reduced in FFT in

the order of 𝑁

2𝑙𝑜𝑔2 N from N 𝑙𝑜𝑔2 N in DFT.More

Computation time is required for sweeping all frequency

components to compute the specified frequency of interest.

Reordering of input signal i.e. Bit-Reversal order is required

to perform FFT. Complexity has increased on increasing the

transformation length.

B. Applications of Goertzel Algorithm

Goertzel Algorithm especially applicable in the field of

single tone and DTMF (Dual Tone Multi-frequency)

detection in touch-tone telephones to represent the digits

corresponding to the user push buttons as well as it is

suitable for computer applications such as voice mail,

telephone banking, pager systems, email application and

interactive control applications such as conference calling

and call forwarding.

B.1 Advantages of Goertzel Algorithm

Goertzel Algorithm is more suitable in DTMF applications

which require only few spectral components for detecting

frequencies instead of computing whole spectrum. In this

area, Goertzel Algorithm is significantly faster and also it

requires only few constants needs to compute. So, that it

saves computation time, reducing hardware complexity and

avoiding Complex algebra. Also, Goertzel Algorithm does

not require reordering of data in input and output side.

Frequency resolution can be achieved exactly for desired

input signals over FFT. Disadvantages of Goertzel

algorithm is frequency index can compute only for known

set of frequencies and not suitable for random noise input

signals for unknown frequencies.

IV IMPLEMENTATION OF FM MODULATOR IN

XSG

Xilinx system Generator block set integrated with

Matlab Simulink is used in this project for

implementation.

Generation of Sine Wave

From the basic block of system generator i.e. addsub,

constant, mult, rom and shift blocks, we can generate

sine wave of desired frequency as shown in the Fig.

6.

Fig. 6. Generation of Sine Wave in XSG

For example, consider if we want to generate a sine

wave of 'fd ' = 1KHz frequency we need to calculate

constant ' C ' value as

fd = 1KHz

size of addsub block is 'n' bit=16

fs=200KHz

𝐶 =(2𝑛 − 1) ∗ fd

fs

therefor 𝐶 =(216−1)∗1K

200K = 327.675

So when the constant value is given as 327.675, and

run the program it will generate 1 KHz frequency of

saw tooth signal ranging from 0 to 65535 as shown in

the Fig. 7.

ISSN: 2278 – 909X



685


Fig. 7. Simulation of Saw Tooth Signal of 1 KHz

Frequency

Fig. 8. Read only Memory Parameter Box

Read only memory (ROM) block will convert saw

tooth wave to sine wave and its parameter are to be

set according to the Fig. 8.

Depth = 216

Initial Vector Value 32767*sin(2*pi*[0:1/65535:1]) in order

to generate sine wave

When the saw tooth signal is given to ROM block, it will

convert saw tooth wave to sine wave and shifting range by

shift block with parameter 15 shift, will results in 1V p-p

sine wave of 1 KHz frequency as shown in Fig. 9.

Fig. 9. Simulation of Sine wave Signal of 1 KHz

Frequency.

A. Generation of FM Signal

Generation of FM signal is similar to generation of

sine wave, which also include similar block sets as

shown in Fig. 10.

Fig. 10. Generation of FM Wave in XSG

Here 2 constants are necessary to calculate say 'C 1 '

and „C2‟. For example

fc = 20KHz

size of addsub block is 'n' bit =16

fs=200KHz

Δf=10KHz

𝐶1 =(2𝑛−1)∗fc

fs (13)

𝐶2 = 2𝑛−1 ∗(fc +∆ f)

fs−

(2𝑛−1)∗fd

fs (14)

ISSN: 2278 – 909X



686


𝐶1 =(216−1)∗20K

200K = 655 , and

𝐶2 = 216−1 ∗(20K+∆10k)

200K−

(216−1)∗20K

200K = 3276.75

Setting the constant value according to the above

calculated value, FM signal is generated with carrier

frequency fc = 20 KHz and Δf =10KHzwhich is as

shown in Fig. 11.

Fig. 11. Top Level block diagram for Frequency

Modulator using System Generator

Fig. 12. Simulation of FM Signal in XSG

B.System Generator model for FFT based Frequency

Demodulation

Fig. 13. System Generator model design for Frequency

demodulators

The Xilinx Fast Fourier Transform 7.1 block implements an

efficient algorithm for computing the Discrete Fourier

Transform (DFT). The N-point (where, N = 2𝑚 , m = 3 –

16) forward or inverse DFT (IDFT) is computed on a vector

of N complex values represented using data width from 8 to

34, inclusive). The transform computation uses the Cooley-

turkey decimation in time algorithm for the Burst I/O

architectures, and Decimation in Frequency for the

pipelined and Streaming I/O architectures.

C. Results Analysis of FFT

1) Input frequency = 2KHZ, with sampling frequency of

50 KHZ.

Fig. 14. Simulation analysis for Peak detection using

FFT

ISSN: 2278 – 909X



687


Done pin at 0.9134 in x - axis, the difference between done pin

and next peak values of the FFT signal (0.9138 - 0.9134) is

0.0004

2) Input frequency = 2KHZ, with sampling frequency of 50

KHZ

Fig. 15. Simulation Analysis for Peak detection using

FFT

Done pin at 0.9134 in x - axis, the difference between done

pin and next peak values of the FFT signal (0.9154 - 0.9134)

is 0.0020 which is five times of the input signal x(n) i..e 2

KHZ.

D. System Generator model for Goertzel based Frequency

Demodulation

The system generator model realization for FM demodulator

module using Goertzel algorithm is depicted in Fig. 13. In

order to design one Goertzel blocks, one complex

multiplier, set of multipliers, delays and adders/sub tractors

are required which is designed from system generator

library. For computing argmax𝑘 X[k],seven set of M-code

Block sets are used for performing simple comparator

operations to finding frequency bin corresponding to input

FM signal. For frequency estimation and final stage process

has been carried out as same as FFT explained above.

Fig. 16. System Generator model design for Frequency

demodulators using Goertzel Algorithm

Fig. 17. System Generator model design for Goertzel for

detecting a single frequency

In Goertzel based demodulation, based on the magnitude a

particular frequency is detected. If user designed Goertzel

algorithm for a specified frequency, three important

parameters are to be considered. One is frequency index, k,

which is to be easily calculated if we know the frequency of

the signal to be detected. In this design, frequency index is

pre-calculated based on the known input and sampling

frequency relation „k‟. The X[k], magnitude is maximum

only the particular frequency, other than that its value is

negligible. So, based on the magnitude of the signal we can

detect the particular block which is to be detected. Other

two parameters are cosine terms and twiddle factors can be

calculated based on the appropriate frequency detection.

ISSN: 2278 – 909X



688


In order to detect the frequencies, modulator is designed

using FM techniques. Based on the counter limited signal,

the number of frequencies is to be generated. The Goertzel

blocks are designed and coefficients are pre-computed to

detect various frequencies. Once if it is detected the

appropriate frequency index values are considered as output.

In this way, all the eight Goertzel blocks are detected one

after another and corresponding frequency index is chosen.

This logic is built using MATLAB M-code and it is

embedded into the Xilinx blocks using if-else condition.

After computing frequency index passing through self-built

M-code block and it is multiplied with 𝐹𝑠 / N, to compute

the frequency of the input signal to be detected. This process

is continuous for detecting eight different frequencies to be

detected. This can be extended to detect „N‟ number of

frequencies. The frequencies are converted back into full-

pledged demodulated signal.

V EXPERIMENTAL RESULTS

A. Simulation results for FFT based frequency

demodulation

The simulation waveforms of the FFT based frequency

demodulator is shown in Fig. 18. The counter signal is given

as input to the modulator and the modulator waveform as

shown in fig. In order to show better visibility of

waveforms to see clearly, a counter signal 2-bit is

considered as input to the FM modulator. In Fig. 18, the first

waveform is counter limited input signal fed to the

Frequency modulator, second waveform is the frequency

modulator from modulator design, third waveform is FFT,

the magnitude of output X[k] from FFT blocks which has

real and imaginary components to an applied input signal,

followed by the value of k, corresponding to maximum

values of X[k] based on the number of FFT points on FFT

block. Frequency detection is done with the relation and the

value of 'k' obtained from FFT block and frequency to

voltage conversion based on the logic explained earlier.

Fig. 18. Simulation results of FFT based Frequency

Demodulator

B. Simulation results for Goertzel block based Frequency

Demodulation

Similarly the simulation waveform results of the Goertzel

based frequency demodulator is shown in Fig. 19. In Fig.

19, the first waveform is input signal fed to the Frequency

modulator from external counter signal to the modulator

block as input, second waveform is the frequency output,

which is based on the counter bit signal the waveform is

generated inside on the modulator block. For example, if

you provide 2 bit counter as an input to the modulator, four

steps from 0 to 3 is generated in the counter and that is

given as a input to the modulator block. For every step,

there is a generation of frequency with the frequency

deviation. Here, frequency deviation is considered as 1

KHz. so, for the first step it will generate 1 KHz which is

added to previous generated sine wave frequencies. The

next consecutive four waveforms represent the Goertzel

block output X[k] computed from 2nd order filter designed

based on the parameter set into the filter block. The value of

X[k] which is high only for specified detected Goertzel

block and other Goertzel block magnitude value is very less

compared to detected frequency energy. The next

waveforms Goertzel frequency index 'k' value and next

waveform is frequency detection, it is done based frequency

index value and logic is implemented explained in previous

chapter. Based on the frequency detection, it is converted

into the corresponding voltage value.

ISSN: 2278 – 909X



689


Fig. 19. Simulation results of Goertzel block based

Frequency Demodulator

VI. CONCLUSION

In this paper, design of frequency demodulators for Fast

Fourier transform, Goertzel Block Algorithm methods are

proposed. A detail about the performance evaluation and

algorithm design development for the proposed work is

reported in this paper. It is observed that Goertzel blocks

simulation and algorithm design development is compared

in terms of simulation results with standard FFT based

demodulation techniques. It is observed that the proposed

frequency demodulators worked satisfactorily for all above

mentioned methods and the same can be employed for

various industrial applications. In application, that requires

minimum number of blocks for design and implement in

hardware Goertzel demodulator is the best choice.

VII. REFERENCES

[1] Mrs. Mahmooda, M. Vinod Kumar Reddy, Sagar Nayakanti,

paper titled "Implementation of Spectrum Analyzer using

Goertzel Algorithm", 2013, International Journal of Scientific

and Research Publications, Volume 3, Issue 3, ISSN 2250-3153,

March. 2013.

[2] D. Divya, MRS. M. A. Asima begum, G. Kalyan, paper titled,

"DTMF Signal Generation and Detection Using Effective DFT

(Goertzel algorithm) Technique on FPGA", 2015, International

journal of Science, Engineering and Technology Research

(IJSETR) , Volume 4, Issue 11, ISSN 2278-7798, November.

2015.

[3] Anis W R, "FM and FSK detection using a subtractor filter" a

IEEE paper in Circuits of Electronics and Systems, 2005, ICECS

2005 on (Volume: 2), the 7th International IEEE Conference.

[4] Bampi Sergio and Pablo Juan Brito Martinez, "Design of a

Digital FM (DFM) Demodulator based on a All-Digital Phase-

Locked Loop with filter order 2" PGMICRO – Graduate Program

on Microelectronics Federal University of Rio Grande do Sul,

UFRGS.

[5] P Sumathi, IEEE paper on “A Frequency Demodulation (FM

demodulation) Technique Based on Sliding Direct Fourier

Transform (DFT) Phase Locking Scheme for FM Signals”.

Rahul Shetty, B.E in Electronics and Communication Engineering, Sahyadri College of Engineering and Management,

Mangalore- 575007. Pavanalaxmi, Assistant Professor, Dept. of E & C, Sahyadri College of Engineering and Management, Mangaluru-575007.

.

design of frequency demodulator using goertzel...

Documents