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sh

Digital Signal

Processing

Vikas Kumar

C07558EECE, 7th SEM

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Digital Signal Processing

EXPERIMENT NO. 1

EXPERIMENT 1(a)

Aim : Write a program to generate a sine wave.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

x=linspace(0,2*pi,100);

plot(x,sin(x))

xlabel('x-axistime');ylabel('sin(x)');

title('sinewave');

axis('equal');

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 1(b)

Aim : Write a program to generate space curve.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

x=linspace(0,2*pi,100);

plot3(cos(x),sin(x),x)

xlabel('x');

ylabel('y');

zlabel('z');zlatitle('spacecurve');

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 1(c)

Aim : Write a program to plot a circle.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

r=1;

theta=linspace(0,2*pi,100);

x=r*sin(theta);y=r*cos(theta);

plot(x,y)

xlabel('x');

ylabel('y');

title('circle');

axis('equal');

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 1(d)

Aim : Write a program to plot graphs using subplot command.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

t=linspace(0,2*pi,100);

x=cos(t);

y=sin(t);z=tan(t);

k=exp(t);

subplot(1,4,1);

plot(t,x)

grid on;

axis('equal');

xlabel('time');

ylabel('cos(t)');

title('graph1');

subplot(1,4,2);

plot(t,y)grid on;

axis('equal');

xlabel('time');

ylabel('sin(t)');

title('graph2');

subplot(1,4,3);

plot(t,z)

grid on;

axis('equal');

xlabel('time');

ylabel('tan(t)');

title('graph3');

subplot(1,4,4);

plot(t,k)

grid on;

axis('equal');

xlabel('time');

ylabel('exp(t)');

title('graph4');

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Digital Signal Processing

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 1(e)

Aim : Using MATLAB commands perform the various matrix operations.

Apparatus: MATLAB version 7.

>> x=[1,2,3;4,5,6;7,8,9] (x matix of order 3*3)

x =

1 2 3

4 5 6

7 8 9

>> x*x (multiplication of x matrix with itself)

ans =

30 36 42

66 81 96

102 126 150

>>x' (transpose of x matrix)

ans =

1 4 7

2 5 8

3 6 9

>> x*x' (multiplication of x matrix with its transpose)

ans =

14 32 50

32 77 122

50 122 194

>> x.*x' (element by element multiplication)

ans =

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Digital Signal Processing

1 8 21

8 25 48

21 48 81

>> eye(3) (identity matrix of order 3)

ans =

1 0 0

0 1 0

0 0 1

>> diag(x) (diagonal elements of x matrix)

ans =

1

5

9

>> x^2 (multiplication of x matrix with itself)

ans =

30 36 42

66 81 96102 126 150

>> [eigvec,eigval]=eig(x) (eigen values and eigen vectors of x matrix)

eigvec =

-0.2320 -0.7858 0.4082

-0.5253 -0.0868 -0.8165

-0.8187 0.6123 0.4082

eigval =

16.1168 0 0

0 -1.1168 0

0 0 -0.0000

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Digital Signal Processing

EXPERIMENT NO. 2

EXPERIMENT 2(a)

Aim : Write a program to plot unit impulse function.

Apparatus: MATLAB version 7.

Program Code:clc;

clearall;

close all;

t=-9:1:9;

y=[zeros(1,9),ones(1,1),zeros(1,9)];

stem(t,y);

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 2(b)

Aim : Write a program to plot unit step function.

Apparatus: MATLAB version 7.

Program Code:

clc;clearall;

close all;

n=input('enter value of n');

t=0:1:n-1;

y=ones(1,n);

stem(t,y);

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 2(c)

Aim : Write a program to plot a ramp function.

Apparatus: MATLAB version 7.

Program Code:clc;

clearall;

close all;

n=input('enter value of n');

t=0:n;

stem(t,t);

grid on;

Output:

enter value of n6

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Digital Signal Processing

Output Window:

EXPERIMENT 2(d)

Aim : Write a program to plot linear convolution function.

Apparatus: MATLAB version 7.

Program Code:

clc;

clearall;

close all;

x=input('enter first sequence');

h=input('enter second sequence');

y=conv(x,h);

subplot(1,3,1)

stem(x);

xlabel('t');

ylabel('x');

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Digital Signal Processing

subplot(1,3,2)

stem(h);

xlabel('t');

ylabel('h');

subplot(1,3,3)stem(y);

xlabel('t');

ylabel('y');

display('the result is: ');

y

grid on;

Output:

enter first sequence[1,2,3,4]

enter second sequence[1,1,1,1]

Output Window:

Manish Bansal

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Digital Signal Processing

Result:

the result is:

y =

1 3 6 10 9 7 4

EXPERIMENT 3

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Digital Signal Processing

Aim : Write a program to perform linear convolution and plot a graph for the

resultant function.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

a=input('enter the value of a');

b=input('enter the value of b');

m1=input('enter the range of a');

m2=input('enter the range of b');

stem(m1,a)

figure;stem(m2,b)

figure;

m=m1(1,1)+m2(1,1);

n=m1(1,end)+m2(1,end);

j=[m:1:n];

c=conv(a,b);

stem (j,c)

c

Output:

enter the value of a[2,3,4,5,6]

enter the value of b[-4,-7,-5,3]

enter the range of a[-1:1:3]

enter the range of b[-2:1:1]

c =

-8 -26 -47 -57 -70 -55 -15 18

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Digital Signal Processing

Output Window:

Manish Bansal

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Digital Signal Processing

Manish Bansal

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Digital Signal Processing

EXPERIMENT 4(a)

Aim : Write a program to calculate inverse z-transform of a given sequence.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

a=[1,0.2,0.5];

b=[1,-0.5];

n=4;

a=[a zeros(1,n-1)];x=deconv(a,b);

stem(x);

x

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

Result:

the result is

x =

1.0000 0.7000 0.8500 0.4250 0.2125

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Digital Signal Processing

EXPERIMENT 4(b)

Aim : Write a program to calculate inverse z-transform of a given sequence.

Apparatus: MATLAB version 7.

Program Code:

clc;

clear all;

close all;

a=[2,3,4];

b=[1,-1.5,-3.5];n=5;

b=[b zeros(1,n-1)];

x=deconv(b,a);

disp(x);

stem(x);

x

grid on;

Output Window:

Manish Bansal

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Digital Signal Processing

Result:

the result is

x =

0.5000 -1.5000 -0.5000 3.7500 -4.6250

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Digital Signal Processing

EXPERIMENT 5(a)

Aim : Write a sequence to calculate DFT of a given sequence using MATLAB

software.

Apparatus: MATLAB version 7.

Program Code:

clc;

close all;

clear all;

x=input('input the sequence');

y=input('enter the length of the sequence');

z=fft(x,y);

stem(z);

z

Command Window:

input the sequence [1,2,3,4,5]

enter the length of the sequence 8

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Digital Signal Processing

z =

Columns 1 through 4

15.0000 -5.4142 - 7.2426i 3.0000 + 2.0000i -2.5858 - 1.2426i

Columns 5 through 8

3.0000 -2.5858 + 1.2426i 3.0000 - 2.0000i -5.4142 + 7.2426i

>>

Output Window:

Manish Bansal

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Digital Signal Processing

EXPERIMENT 5(b)

Manish Bansal

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Digital Signal Processing

Aim : Write a sequence to calculate IDFT of a given sequence using MATLAB

software.

Apparatus: MATLAB version 7.

Program Code:

clc;

close all;

clear all;

x=input('input the sequence');

y=input('enter the length of the sequence');

z=ifft(x,y);

stem(z);

z

Command Window:

input the sequence[1,2,3,4,5]

enter the length of the sequence 8

z =

Columns 1 through 4

1.8750 -0.6768 + 0.9053i 0.3750 - 0.2500i -0.3232 + 0.1553i

Columns 5 through 8

0.3750 -0.3232 - 0.1553i 0.3750 + 0.2500i -0.6768 - 0.9053i

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Digital Signal Processing

Output Window:

Manish Bansal