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Digital Signal Processing Lab Programs Using Matlab

Digital Signal Processing Lab Programs Using Matlab

1. Linear Convolution

2. Circular Convolution

3. FIR filters

4. IIR filters

5. Fast Fourier Transform

6. Power Spectral Density

7. Sum of Sinusoidal Signals

8. LPF & HPF

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1. Linear Convolution

1. Linear Convolution

AIM:

To verify Linear Convolution.

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

% MATLAB program for linear convolution

%linear convolution program

clc;

clear all;

close all;

disp('linear convolution program');

x=input('enter i/p x(n):');

m=length(x);

h=input('enter i/p h(n):');

n=length(h);

x=[x,zeros(1,n)];

subplot(2,2,1), stem(x);

title('i/p sequence x(n)is:');

xlabel('---->n');

ylabel('---->x(n)');grid;

h=[h,zeros(1,m)];

subplot(2,2,2), stem(h);

title('i/p sequence h(n)is:');

xlabel('---->n');

ylabel('---->h(n)');grid;

disp('convolution of x(n) & h(n) is y(n):');

y=zeros(1,m+n-1);

for i=1:m+n-1

y(i)=0;

for j=1:m+n-1

if(j<i+1)

y(i)=y(i)+x(j)*h(i-j+1);

end

end

end

y

subplot(2,2,[3,4]),stem(y);

title('convolution of x(n) & h(n) is :');

xlabel('---->n');

ylabel('---->y(n)');grid;

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2. Circular Convolution

2. Circular Convolution

AIM: To verify Circular Convolution.

EQUIPMENTS: Operating System – Windows XP    Constructor – Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

%circular convolution program

clc;

clear all;

close all;

disp('circular convolution program');

x=input('enter i/p x(n):');

m=length(x);

h=input('enter i/p sequence h(n)');

n=length(h);

subplot(2,2,1), stem(x);

title('i/p sequencce x(n)is:');

xlabel('---->n');

ylabel('---->x(n)');grid;

subplot(2,2,2), stem(h);

title('i/p sequencce h(n)is:');

xlabel('---->n');

ylabel('---->h(n)');grid;

disp('circular convolution of x(n) & h(n) is y(n):');

if(m-n~=0)

if(m>n)

h=[h,zeros(1,m-n)];

n=m;

end

x=[x,zeros(1,n-m)];

m=n;

end

y=zeros(1,n);

y(1)=0;

a(1)=h(1);

for j=2:n

a(j)=h(n-j+2);

end

%ciruclar conv

for i=1:n

y(1)=y(1)+x(i)*a(i);

end

for k=2:n

y(k)=0;

% circular shift

for j=2:n

x2(j)=a(j-1);

end

x2(1)=a(n);

for i=1:n

if(i<n+1)

a(i)=x2(i);

y(k)=y(k)+x(i)*a(i);

end

end

end

y

subplot(2,2,[3,4]),stem(y);

title('convolution of x(n) & h(n) is:');

xlabel('---->n');

ylabel('---->y(n)');grid;

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3. FIR filters

 3. FIR filters

AIM

To verify FIR filters.

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

%fir filt design window techniques

clc;

clear all;

close all;

rp=input('enter passband ripple');

rs=input('enter the stopband ripple');

fp=input('enter passband freq');

fs=input('enter stopband freq');

f=input('enter sampling freq ');

wp=2*fp/f;

ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;

dem=14.6*(fs-fp)/f;

n=ceil(num/dem);

n1=n+1;

if(rem(n,2)~=0)

n1=n;

n=n-1;

end

c=input('enter your choice of window function 1. rectangular 2. triangular 3.kaiser: \n ');

if(c==1)

y=rectwin(n1);

disp('Rectangular window filter response');

end

if (c==2)

y=triang(n1);

disp('Triangular window filter response');

end

if(c==3)

y=kaiser(n1);

disp('kaiser window filter response');

end

%LPF

b=fir1(n,wp,y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,1);plot(o/pi,m);

title('LPF');

ylabel('Gain in dB-->');

xlabel('(a) Normalized frequency-->');

%HPF

b=fir1(n,wp,'high',y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,2);plot(o/pi,m);

title('HPF');

ylabel('Gain in dB-->');

xlabel('(b) Normalized frequency-->');

%BPF

wn=[wp ws];

b=fir1(n,wn,y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,3);plot(o/pi,m);

title('BPF');

ylabel('Gain in dB-->');

xlabel('(c) Normalized frequency-->');

%BSF

b=fir1(n,wn,'stop',y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,4);plot(o/pi,m);

title('BSF');

ylabel('Gain in dB-->');

xlabel('(d) Normalized frequency-->');

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4. IIR filters

4. IIR filters

AIM

To design and implement IIR (LPF/HPF)filters.

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

% IIR filters LPF & HPF

clc;

clear all;

close all;

disp('enter the IIR filter design specifications');

rp=input('enter the passband ripple');

rs=input('enter the stopband ripple');

wp=input('enter the passband freq');

ws=input('enter the stopband freq');

fs=input('enter the sampling freq');

w1=2*wp/fs;w2=2*ws/fs;

[n,wn]=buttord(w1,w2,rp,rs,'s');

c=input('enter choice of filter 1. LPF 2. HPF \n ');

if(c==1)

disp('Frequency response of IIR LPF is:');

[b,a]=butter(n,wn,'low','s');

end

if(c==2)

disp('Frequency response of IIR HPF is:');

[b,a]=butter(n,wn,'high','s');

end

w=0:.01:pi;

[h,om]=freqs(b,a,w);

m=20*log10(abs(h));

an=angle(h);

figure,subplot(2,1,1);plot(om/pi,m);

title('magnitude response of IIR filter is:');

xlabel('(a) Normalized freq. -->');

ylabel('Gain in dB-->');

subplot(2,1,2);plot(om/pi,an);

title('phase response of IIR filter is:');

xlabel('(b) Normalized freq. -->');

ylabel('Phase in radians-->');

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5. Fast Fourier Transform

5. Fast Fourier Transform

AIM:

To verify Fast Fourier Transform.

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

%fast fourier transform

clc;

clear all;

close all;

tic;

x=input('enter the sequence');

n=input('enter the length of fft');

%compute fft

disp('fourier transformed signal');

X=fft(x,n)

subplot(1,2,1);stem(x);

title('i/p signal');

xlabel('n --->');

ylabel('x(n) -->');grid;

subplot(1,2,2);stem(X);

title('fft of i/p x(n) is:');

xlabel('Real axis --->');

ylabel('Imaginary axis -->');grid;

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6. Power Spectral Density

 6. Power Spectral Density

AIM:

To verify Power Spectral Density

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

%Power spectral density

t = 0:0.001:0.6;

x = sin(2*pi*50*t)+sin(2*pi*120*t);

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

figure,plot(1000*t(1:50),y(1:50))

title('Signal Corrupted with Zero-Mean Random Noise')

xlabel('time (milliseconds)');

Y = fft(y,512);

%The power spectral density, a measurement of the energy at various frequencies, is:

Pyy = Y.* conj(Y) / 512;

f = 1000*(0:256)/512;

figure,plot(f,Pyy(1:257))

title('Frequency content of y');

xlabel('frequency (Hz)');

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7. Sum of Sinusoidal Signals

7. Sum of Sinusoidal Signals

AIM:

To verify Sum of Sinusoidal Signals using MATLAB

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

PROGRAM:

% sum of sinusoidal signals

clc;

clear all;

close all;

tic;

%giving linear spaces

t=0:.01:pi;

% t=linspace(0,pi,20);

%generation of sine signals

y1=sin(t);

y2=sin(3*t)/3;

y3=sin(5*t)/5;

y4=sin(7*t)/7;

y5=sin(9*t)/9;

y = sin(t) + sin(3*t)/3 + sin(5*t)/5 + sin(7*t)/7 + sin(9*t)/9;

plot(t,y,t,y1,t,y2,t,y3,t,y4,t,y5);

legend('y','y1','y2','y3','y4','y5');

title('generation of sum of sinusoidal signals');grid;

ylabel('---> Amplitude');

xlabel('---> t');

toc;

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8. LPF & HPF

8. LPF & HPF

AIM:

To verify response of analog LPF & HPF using MATLAB

EQUIPMENTS:

Operating System – Windows XP

Constructor - Simulator

Software - CCStudio 3 & MATLAB 7.5

 PROGRAM:

% IIR filters LPF & HPF

clc;

clear all;

close all;

warning off;

disp('enter the IIR filter design specifications');

rp=input('enter the passband ripple');

rs=input('enter the stopband ripple');

wp=input('enter the passband freq');

ws=input('enter the stopband freq');

fs=input('enter the sampling freq');

w1=2*wp/fs;w2=2*ws/fs;

[n,wn]=buttord(w1,w2,rp,rs,'s');

c=input('enter choice of filter 1. LPF 2. HPF \n ');

if(c==1)

disp('Frequency response of IIR LPF is:');

[b,a]=butter(n,wn,'low','s');

end

if(c==2)

disp('Frequency response of IIR HPF is:');

[b,a]=butter(n,wn,'high','s');

end

w=0:.01:pi;

[h,om]=freqs(b,a,w);

m=20*log10(abs(h));

an=angle(h);

figure,subplot(2,1,1);plot(om/pi,m);

title('magnitude response of IIR filter is:');

xlabel('(a) Normalized freq. -->');

ylabel('Gain in dB-->');

subplot(2,1,2);plot(om/pi,an);

title('phase response of IIR filter is:');

xlabel('(b) Normalized freq. -->');

ylabel('Phase in radians-->');

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