Experiment NO:-6 Date:-

Program:-1(A)

 AIM:- Write a MATLAB code for different types of Signal Generation

 MATLAB CODE:-

% <----------Signal Generation------------>

clc;

close all;

%<------STEP SIGNAL----->

t=-1:0.001:1;

x=(t>=0);

subplot(3,2,1);

plot(t,x);

title('step signal is:');

ylabel('amplitude');

xlabel('time index');

%<------RAMP SIGNAL----->

t=-0:0.001:5;

x=t;

subplot(3,2,2);

plot(t,x);

1
title('ramp signal is:');

ylabel('amplitude');

xlabel('time index');

%<------SINE SIGNAL----->

x=0:0.005:20;

subplot(3,2,3);

plot(x,sin(x));

title('sine signal is:');

ylabel('amplitude');

xlabel('time index');

%<------COSINE SIGNAL---->

x=0:0.001:20;

subplot(3,2,4);

plot(x,cos(x));

title('cosine signal is:');

ylabel('amplitude');

xlabel('time index');

%<-----TRIANGLE PULSE----->

x=-0.5:0.001:0.5;

y = tripuls(x)

2
subplot(3,2,5)

plot(x,y)

title('triangle signal is:');

ylabel('amplitude');

xlabel('time index');

 COMMAND WINDOW:

Columns 1 through 9

0 0.0020 0.0040 0.0060 0.0080 0.0100 0.0120 0.0140

Columns 10 through 18

0.0180 0.0200 0.0220 0.0240 0.0260 0.0280 0.0300 0.0320

0.0340

Columns 19 through 27

0.0360 0.0380 0.0400 0.0420 0.0440 0.0460 0.0480 0.0500

0.0520

Columns 28 through 36

0.0540 0.0560 0.0580 0.0600 0.0620 0.0640 0.0660 0.0680

0.0700

3
 FIGURE:-

4
Program:-1(B) Date:-

 AIM:- Write a MATLAB code for different types of Signal Operations

 MATLAB CODE:-

%<------SIGNAL OPERATIONS------>

clc;

close all;

figure(1);

%<-----Sine signal----->

x=0:0.001:10;

subplot(4,2,1);

plot(x,sin(x))

title('Sine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Compression of Sine signal----->

x=0:0.001:10;

subplot(4,2,2);

plot(x,sin(x*2))

5
title('Compressed sine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Expansion of Sine signal----->

x=0:0.001:20;

subplot(4,2,3);

plot(x,sin(x/2))

title('Expanded sine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Shifting of Sine signal----->

x=0:0.001:20;

subplot(4,2,4);

plot(x,sin(x+5))

title('Shifted sine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Cosine Signal----->

x=0:0.001:10;

subplot(4,2,5);

6
plot(x,cos(x))

title('Cosine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Compression of Cosine signal----->

x=0:0.001:10;

subplot(4,2,6);

plot(x,cos(x*2))

title('Compressed cosine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Expansion of Cosine signal----->

x=0:0.001:20;

subplot(4,2,7);

plot(x,cos(x/2))

title('Expanded cosine signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Shifting of Cosine signal----->

x=0:0.001:20;

7
subplot(4,2,8);

plot(x,cos(x+5));

title('Shifted cosine signal:');

ylabel('amplitude');

xlabel('time index');

figure(2);

%<-----Step Signal----->

t=-5:0.001:5;

x=(t>=0)

subplot(4,2,1);

plot(t,x);

title('Step signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Shifting of step signal----->

t=-5:0.001:5;

x=(t>=2)

subplot(4,2,2);

plot(t,x);

title('Shifted step signal:');

ylabel('amplitude');

8
xlabel('time index');

%<-----Ramp Signal----->

t=-5:0.001:5;

x=t

subplot(4,2,3);

plot(t,x);

title('Ramp signal:');

ylabel('amplitude');

xlabel('time index');

%<-----Shifting of Ramp signal----->

t=-5:0.001:5;

x=t/4

subplot(4,2,4);

plot(t,x);

title('Shifted ramp signal:');

ylabel('amplitude');

xlabel('time index'):

 COMMAND WINDOW:
x=

Columns 1 through 9

-5.0000 -4.9900 -4.9800 -4.9700 -4.9600 -4.9500 -4.9400 -4.9300

9
-4.9200

Columns 10 through 18

-4.9100 -4.9000 -4.8900 -4.8800 -4.8700 -4.8600 -4.8500 -4.8400

-4.8300

Columns 19 through 27

-4.8200 -4.8100 -4.8000 -4.7900 -4.7800 -4.7700 -4.7600 -4.7500

Columns 28 through 36

-4.7300 -4.7200 -4.7100 -4.7000 -4.6900 -4.6800 -4.6700 -4.6600

 FIGURE:

10
11
Experiment NO:-7 Date:-
Program:-2

 AIM:- Write a MATLAB code for ENERGY & POWER Signal calculations

 MATLAB CODE:-

%<--------Energy Calculations of Aperiodic siganl(Ramp)------->

%<------Ramp Signal------>

figure(1);

t=-1:0.01:1;

x=t;

subplot(3,1,1);

plot(t,x);

grid;

xlabel('t');

ylabel('x(t)');

%<------Energy of Ramp Signal----->

subplot(3,1,2);

plot(t,x.^2);

xlabel('t');

ylabel('x^2(t)');

12
title('Energy of Ramp signal')

axis([-1 1 -.2 1.5]);

grid;

%<-----Energy-Area under signal----->

subplot(3,1,3);

area(t,x.^2);

xlabel('t');

ylabel('x^2(t)');

title('The colored area gives the energy')

axis([-1 1 -.2 1.1]);

grid;

%<-------Power Calculations of Aperiodic Signal(Sine)----->

t=-2:0.01:2;

x1=sin(2*pi*t);

n=-40:40;

x2=sin(pi*(1/10)*n);

%<------Analog Sine Signal------>

figure(2);

subplot(2,1,1)

plot(t,x1);

grid on;

13
title('Analog & Discrete sine');

xlabel('t');

ylabel('x_1(t)');

%<------Descrete Sine Signal------>

subplot(2,1,2);

stem(n,x2);

grid on;

xlabel('n');

ylabel('x_2(n)');

%<------Power of Sine Signal------->

figure(3);

subplot(2,1,1);

plot(t,x1.^2); %Energy of X1

grid on;

hold on

% red lines marking 0 & 1

plot([0 0], [-.2 1.2],'g', [1 1], [-.2 1.2],'g');

hold off

axis([-2 2 -.2 1.2]);

title('Squared sines');

xlabel('t');

14
ylabel('x_1^2(t)');

subplot(2,1,2);

stem(n,x2.^2); %Energy of X2

grid on;

hold on;

% red lines marking 1 & 20

plot([1 1], [-.2 1.2],'r', [20 20], [-.2 1.2],'r');

hold off;

axis([-40 40 -.2 1.2]);

xlabel('n');

ylabel('x_2^2(n)');

%calculating power of one period of X1.

%disp('Power, one period:');

%P1 = (1/1)*sum(x1(1:1).^2)

%calculating power of one period of X2.

disp('Power, one period:');

P2 = (1/20)*sum(x2(1:20).^2)

15
 COMMAND WINDOW:

Power, one period:

P2 =0.5000

 FIGURE:-

16
17
Experiment NO:-8 Date:-
Program:-3
 AIM:- Write a MATLAB code for Auto Co-Relation & Cross Co-Relation

 MATLAB CODE:-

%-----------------------------------------

clc;

close all;

clear all;

%--------------------------------

a=[1 0 2]

b=[1 1 2]

c=xcorr(a,b)

d=xcorr(a,a)

e=xcorr(b,b)

%<-----------Sine Signal----------->

x=0:0.1:25;

subplot(3,2,1);

w=sin(x);

plot(x,w);grid;

title('sine signal is:');

18
ylabel('amplitude');

xlabel('time index');

%<------COSINE SIGNAL---->

subplot(3,2,2);

v=cos(x);

plot(x,v);grid

title('cosine signal is:');

ylabel('amplitude');

xlabel('time index');

%<-----Co-relations of signals----->

subplot(3,2,3);

p=xcorr(w,v)

plot(p);grid;

subplot(3,2,4);

q=xcorr(w,w)

plot(q);grid;

subplot(3,2,5);

r=xcorr(v,v)

plot(r);grid;

19
 COMMAND WINDOW:
a= 1 0 2

b= 1 1 2

c= 2.0000 1.0000 5.0000 2.0000 2.0000

d= 2 0 5 0 2

e= 2 3 6 3 2

p=

Columns 1 through 9

-0.0000 0.0990 0.2941 0.5806 0.9519 1.3998 1.9142 2.4836

Columns 10 through 18

3.7358 4.3899 5.0426 5.6780 6.2802 6.8334 7.3221 7.7314

Columns 19 through 27

8.2572 8.3491 8.3131 8.1409 7.8259 7.3638 6.7524 5.9916

20
Columns 28 through 36

q=

Columns 1 through 9

0.0000 -0.0132 -0.0493 -0.1175 -0.2265 -0.3838 -0.5964 -0.8698

Columns 10 through 18

-1.6150 -2.0912 -2.6370 -3.2506 -3.9287 -4.6665 -5.4574 -6.2934

Columns 19 through 27

-8.0616 -8.9709 -9.8800 -10.7748 -11.6407 -12.4625 -13.2248

r=

Columns 1 through 9

0.9912 1.9593 2.8848 3.7488 4.5335 5.2223 5.7998 6.2526

Columns 10 through 18

6.7396 6.7572 6.6168 6.3162 5.8554 5.2372 4.4669 3.5524

Columns 19 through 27

1.3338 0.0571 -1.3095 -2.7476 -4.2369 -5.7561 -7.2828 -8.7939

21
 FIGURE:

22
Experiment NO:-9 Date:-
Program:-4

 AIM:- Write a MATLAB code for finding Exponential and Trigonometric

 MATLAB CODE:-

%<-------To Find Exponential Fourier series Co-efficient------->

%M is the number of coefficients to be computed

clc;

close all;

clear all;

%-----------------------------------

T0=pi;

N0=40;

Ts=T0/N0;

M=10;

t=0:Ts:Ts*(N0-1);

t=t';

g=exp(-t/2);

g(1)=0.604;

Dn=fft(g)/40; % Dn is the Samples of g(t) over ONE PERIOD

[Dnangle,Dnmag]=cart2pol(real(Dn),imag(Dn));

23
k=0:39;

k=k';

figure(1);

subplot(2,1,1)

stem(k,Dnmag);grid

title('Amplitude spectrum');

ylabel('Dn');

xlabel('w');

subplot(2,1,2)

stem(k,Dnangle);grid

title('Phase spectrum');

ylabel('Angle');

xlabel('w');

%<-------To find Trigonometric Fourier Series coefficients------->

c0=Dnmag(1) % c0=Dnmag(1)=ao

Cn=2*Dnmag(2:M); % Cn for M= 2 to 10 (Because Cn(M=1)=c0

Amplitudes=[c0;Cn] % c0 to Cn total 10 amplitude

Angles=Dnangle(1:M); % c0 to Cn total 10 Angles (Because M=10)

Angles=Angles*(180/pi)

%<-------To plot the Fouries coefficients------>

24
k=0:9; % k= 0:length(Amplitudes)-1

k=k';

figure(2);

subplot(2,1,1)

stem(k,Amplitudes);grid;

title('Amplitude spectrum');

ylabel('Cn');

xlabel('w');

subplot(2,1,2)

stem(k,Angles);grid;

title('Phase spectrum');

ylabel('Angle');

xlabel('w');

 COMMAND WINDOW:

Dn =
0.5043
0.0297 - 0.1184i
0.0078 - 0.0615i
0.0035 - 0.0410i
0.0020 - 0.0304i
0.0013 - 0.0238i
0.0009 - 0.0194i
0.0007 - 0.0161i
0.0006 - 0.0136i
0.0005 - 0.0116i
0.0004 - 0.0099i

25
0.0003 - 0.0085i
0.0003 - 0.0072i
0.0003 - 0.0061i
0.0002 - 0.0050i
0.0002 - 0.0041i
0.0002 - 0.0032i
0.0002 - 0.0024i
0.0002 - 0.0016i
0.0002 - 0.0008i
0.0002
0.0002 + 0.0008i
0.0002 + 0.0016i
0.0002 + 0.0024i
0.0002 + 0.0032i
0.0002 + 0.0041i
0.0002 + 0.0050i
0.0003 + 0.0061i
0.0003 + 0.0072i
0.0003 + 0.0085i
0.0004 + 0.0099i
0.0005 + 0.0116i
0.0006 + 0.0136i
0.0007 + 0.0161i
0.0009 + 0.0194i
0.0013 + 0.0238i
0.0020 + 0.0304i
0.0035 + 0.0410i
0.0078 + 0.0615i
0.0297 + 0.1184i

c0 =
0.5043

26
Amplitudes =
0.5043
0.2441
0.1241
0.0822
0.0608
0.0478
0.0388
0.0323
0.0272
0.0232

Angles =
0
-75.9040
-82.7544
-85.0529
-86.1739
-86.8169
-87.2159
-87.4704
-87.6286
-87.7151

27
 FIGURE:

28
29
Experiment NO:-10 Date:-
Program:-5
 AIM:- Write a MATLAB code for finding Fourier Transform of e(-2t) *u(t)

 MATLAB CODE:-

% Fourier transform of e^(-2t)*u(t)

%-----------------------------------------

clc;

close all;

clear all;

%--------------------------------

Ts=1/12;

T0=3;

N0=T0/Ts;

t=0:Ts:Ts*(N0-1);

t=t';

g=Ts*exp(-2*t);

g(1)=Ts*0.5;

G=fft(g)

[Gp,Gm]=cart2pol(real(G),imag(G))

k=0:N0-1;

%k=k';

w=2*pi*k/T0;

30
subplot(2,1,1);

stem(w(1:32),Gm(1:32));

title('Amplitude Spectrum');

ylabel('|G(w)|');

xlabel('w');

subplot(2,1,2);

stem(w(1:32),Gp(1:32))

title('Phase spectrum');

ylabel('Angle');

xlabel('w');

 COMMAND WINDOW:

G=
0.4998
0.2389 - 0.2479i
0.0937 - 0.1915i
0.0470 - 0.1405i
0.0280 - 0.1078i
0.0186 - 0.0858i
0.0134 - 0.0700i
0.0103 - 0.0581i
0.0082 - 0.0487i
0.0068 - 0.0410i
0.0058 - 0.0345i
0.0050 - 0.0288i
0.0045 - 0.0238i
0.0041 - 0.0192i
0.0038 - 0.0150i

31
0.0036 - 0.0111i
0.0035 - 0.0073i
0.0034 - 0.0036i
0.0034
0.0034 + 0.0036i
0.0035 + 0.0073i
0.0036 + 0.0111i
0.0038 + 0.0150i
0.0041 + 0.0192i
0.0045 + 0.0238i
0.0050 + 0.0288i
0.0058 + 0.0345i
0.0068 + 0.0410i
0.0082 + 0.0487i
0.0103 + 0.0581i
0.0134 + 0.0700i
0.0186 + 0.0858i
0.0280 + 0.1078i
0.0470 + 0.1405i
0.0937 + 0.1915i
0.2389 + 0.2479i

Gp =
0
-0.8038
-1.1160
-1.2483
-1.3169
-1.3568
-1.3812
-1.3962
-1.4044
-1.4073
-1.4053

32
-1.3979
-1.3840
-1.3607
-1.3224
-1.2561
-1.1270
-0.8186
0
0.8186
1.1270
1.2561
1.3224
1.3607
1.3840
1.3979
1.4053
1.4073
1.4044
1.3962
1.3812
1.3568
1.3169
1.2483
1.1160
0.8038

Gm =
0.4998
0.3443
0.2132
0.1482
0.1114
0.0878
0.0713

33
0.0590
0.0494
0.0415
0.0349
0.0292
0.0242
0.0197
0.0155
0.0116
0.0081
0.0049
0.0034
0.0049
0.0081
0.0116
0.0155
0.0197
0.0242
0.0292
0.0349
0.0415
0.0494
0.0590
0.0713
0.0878
0.1114
0.1482
0.2132
0.3443

34
 FIGURE:

35