Basic signal processing Matlab codes

7/30/2019 Basic signal processing Matlab codes

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Digital Signal Processor Architecture Lab

Nitish S. Prabhu

1MS10EC071

Table of contents

Analysis of system form it i/o equations .................................................................................................. 1

Impulse response ...................................................................................................................................... 2

Sampling theorem ..................................................................................................................................... 3

FIR filter - window method ....................................................................................................................... 5

IIR Low pass filters .................................................................................................................................... 9

IIR Filter - using bilenear transformation .............................................................................................. 112

Analysis of system form its i/o equations

Compute the magnitude and phase plots form the coefficients of the differential equation.

clc

clear all

close all

b=[1,2,3]; % Feedforward coefficients

a=1; % Feedback coefficients

n=100;

% Plot the Pole-Zero diagram (Fig 1.a)

subplot(4,1,1);

zplane(b,a);

% Plot the frequency response (Fig 1.b)

subplot(4,1,2);

[h,w]=freqz(b,a,n);

plot(h);

% Plot the phase response (Fig 1.c)

subplot(4,1,3);

phase=angle(h);plot(phase);


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% Plot the magnitude response (Fig 1.d)

subplot(4,1,4);

mag=abs(h);

plot(mag);

Fig.1 :Plots for a given i/o differential equation

Impulse response

To determine the impulse response of a given system and thus model the behavior of the system

clc

clear all

close all

n=-20:100; % Discrete time variable

b=1; % Coefficients

a=[1 -0.1 -0.9];

x=(n==0); % Impulse function


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stem(n,x);

title('Filter Output');

figure

y=filter(b,a,x);

stem(n,y)

title('Unit Impulse function');

Sampling theorem

The setup below explains the requirement of fast sampling rates greater than that of Nyquest rates. The

behavior of a system to sampling rates equal to and greater than that of Nyquest frequency is tested.

clc

close all

clear all

f1= 500;

f2= 2000;

% Define the parameters of the signal

N=256;

n=0:N-1;

fs=2*max(f1,f2);

% Case1: Nyquist rate sampling with 'a' and 'b' as input signals

a=sin(2*pi*(f1)*n);


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b=sin(2*pi*(f2)*n);

x=sin(2*pi*(f1/fs)*n)+sin(2*pi*(f2/fs)*n);

nt=n./fs;

% Plot of the sine wave to be sampled

subplot(2,2,1)

plot(nt,x)

xlabel('Time(s)')

ylabel('Amplitude')

title('Sampling at nyquist rate')

grid;

X=fft(x);

mag=abs(X);

fhz=n.*(fs/N);

% The frequecy domain representation

subplot(2,2,3)

plot(fhz(1:N/2),mag(1:N/2));

xlabel('Frequency')

ylabel('Amplitude')

title('Sinewave in freq domain')

grid

% Case2: Sampling at higher rates than Nyquest rate

fh=2*2*max(f1,f2);

z=sin(2*pi*(f1/fh)*n)+sin(2*pi*(f2/fh)*n);

nh=n./fh;

% Plot of the signal to be sampled

subplot(2,2,2)

plot(nh,z);

xlabel('time(seconds)');

ylabel('amplitude');

title('sampling at nyquist rate');grid;

p=fft(x);

mag1=abs(X);

fhz1=n.*(fh/N);


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% The frequency domain representation

subplot(2,2,4)

plot(fhz1(1:N/2),mag(1:N/2));

xlabel('frequency');

ylabel('amplitude');

title('sinewave in freq domain');

grid;

FIR filter - window method

Creating an FIR filter using window method based on the filter specifications like pass band and stop

bang attenuation.

clear all

close all

clc

% Define filter parameters

FS = 8000; % Max frequency


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FN = FS/2; % Nyquest frequency

fp = 1500; % Passband frequency

tw = 500; % Transition Width

fs = fp + tw;

fc = (fp+fs)/2/FN;tw = (fs - fp)/FS;

A = 5; % Stop band Attenuation

for A = 15:15:60

if A21 && A44 && A


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ylabel('Mag resp(dB)');

title(strcat(str,' Window'));

end

Rectangular window :FIR coefficients

Columns 1 through 7

0.0126 0.0188 -0.0066 -0.0246 -0.0026 0.0281 0.0153

Columns 8 through 14

-0.0281 -0.0318 0.0224 0.0537 -0.0067 -0.0878 -0.0358


0.1815 0.3916 0.3916 0.1815 -0.0358 -0.0878 -0.0067


0.0537 0.0224 -0.0318 -0.0281 0.0153 0.0281 -0.0026


-0.0246 -0.0066 0.0188 0.0126

Fig.1 :Frequency response for rectangular window


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Fig.2 : Frequency response for Hanning window

Fig.3 : Frequency response for Hamming winndow

Fig.4 : Frequency response for Blackman window


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IIR Low pass filters

%IIR LPF -- Butterworth characteristic, Impulse invariant transformation

clc

clear all

close all

%N=2, fs=1.28kHz, fc=150Hz

%Filter order

N=2;

%Sampling frequency

fs=1280;

%Cut off frequency

fc=150;

wc=2*pi*fc;

%Analog filter design

[b,a]=butter(N,wc,'s');

disp('Coefficients of analog filter');

disp(b);

disp(a);

[z,p,k]=butter(N,wc,'s');

disp('zeros, poles & gain of analog filter');

disp(z);

disp(p);

disp(k);

%Convert to discrete filter

[bz,az]=impinvar(b,a,fs);

disp('Coefficients of the discrete filter');

disp(bz);

disp(az);

%Plot magnitude response

subplot(2,1,1);

[H,f]=freqz(bz,az,512,fs);

plot(f,20*log10(abs(H)));

grid;

xlabel('Frequency(Hz)');

ylabel('Magnitude response(dB)');


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%plot pole-zero diagram

subplot(2,1,2);

zplane(bz,az);

%Determine poles and zeros

zz=roots(bz);

pz=roots(az);

disp('Zeros and poles of the discrete filter');

disp(zz);

disp(pz);

Coefficients of analog filter

1.0e+05 *

0 0 8.8826

1.0e+05 *

0.0000 0.0133 8.8826

Zeros, poles & gain of analog filter

1.0e+02 *

-6.6643 + 6.6643i

-6.6643 - 6.6643i

8.8826e+05

Coefficients of the discrete filter

0 0.3078 0

1.0000 -1.0308 0.3530

Zeros and poles of the discrete filter

0

0.5154 + 0.2955i

0.5154 - 0.2955i


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IIR Filter - using bilinear transformation

To Design a simple low pass digital IIR filter with Butterworth characteristics to meet the following

specifications Cut off frequency=150Hz, sampling frequency 1.28kHz and filter order 2.

clc

clear all

close all

%IIR LPF -- Butterworth characteristic, Bilinear transformation

%N=2, fs=1.28kHz, fc=150Hz

N=2; %Filter order

fs=1280; %Sampling frequency

fc=150; %Cut off frequency

wc=2*pi*fc;

%Analog filter design -- Normalised Butterworth filter

[b,a]=butter(N,1,'s');

[z,p,k]=butter(N,1,'s');


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%Convert to discrete filter

wc=tan(2*pi*(fc/fs)/2); %Prewarping

%Low pass to low pass transformation

[b1,a1]=lp2lp(b,a,wc);

[bz,az]=bilinear(b1,a1,0.5); %2*Fs=1, Fs=0.5

disp('coefficients of the discrete filter ');

disp(bz);

disp(az);

%Plot magnitude response

subplot(2,1,1);

[H,f]=freqz(bz,az,512,fs);

plot(f,20*log10(abs(H)));

grid;

xlabel('Frequency(Hz)');

ylabel('Magnitude response(dB)');

%plot pole-zero diagram

subplot(2,1,2);

zplane(bz,az);

%determine poles and zeros

[z,p,k]=tf2zp(bz,az);

disp('zeros, poles and gain of the discrete filter');

disp(z);

disp(p);

disp(k);

coefficients of the discrete filter

0.0878 0.1756 0.0878

1.0000 -1.0048 0.3561

Zeros, poles and gain of the discrete filter

-1

-1

0.5024 + 0.3220i

0.5024 - 0.3220i

0.0878


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Basic signal processing Matlab codes

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