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exp -1) generation of unit impulse and unit step signal and sequence

%unit impulse generation and sequence

clc

close all

t=-1:0.01:1;x=(t==0);

subplot(1,2,1)

plot(t,x)

xlabel('n');

ylabel('amplitude');

title('unit impluse signal');

subplot(1,2,2)stem(t,x,'fill')

xlabel('n');


title('unit impulse sequence');

OUTPUT



% generation of unit step signal and sequence

n=-1:0.03:1;

y=(n>=0)

figure;

subplot(1,2,1)

plot(n,y)

grid

title('unit step signal');

xlabel('time');


subplot(1,2,2)

stem(n,y);

gridtitle('unit step sequence');

xlabel('time');


OUTPUT



exp -2) generation of square and sawtooth signal and sequence

% sawtooth wave generator and sequence

fs=10000;

t=0:1/fs:1.5;

x=sawtooth(2*pi*50*t);

subplot(1,2,1);

plot(t,x);

axis([0 0.2 -1 1]);

xlabel('t');

ylabel('x(t)');

title('sawtooth signal');

N=2;

fs=500;

n=0:1/fs:2;

x=sawtooth(2*pi*50*n);

subplot(1,2,2);

stem(n,x);

axis([0 0.2 -1 1]);

xlabel('n');

ylabel('x(n)');

title('sawtooth sequence');



OUTPUT



%square wave generator and sequence

fs=500;

t=0:1/fs:1.5;

x1=square(2*pi*50*t);

subplot(1,2,1);

plot(t,x1);

axis([0 0.2 -1.2 1.2])

xlabel('time(sec)');


subplot(1,2,2);

stem(t,x1);axis([0 0.2 -1.2 1.2])

xlabel('time(sec)');


title('square wave sequence')

OUTPUT



exp -3) generation of ramp signal and sequence

%to generate ramp signal

close all

t=0:1:20;

y=t;subplot(1,2,1)

plot(t,y);

xlabel('t');


title('ramp signal')

subplot(1,2,2)

stem(t,y);xlabel('t');


title('ramp sequence')

OUTPUT



exp -4)generation of sinusoidal and sinc signal and

sequence

%to generate a sinusoidal signal

N=64; %define no. of samplesn=0:N-1; %define vector n=0,1,2,3, .... 63

f=500; %define the frequency

fs=8000; %define the sampling frequency

x=sin(2*pi*(f/fs)*n); % generate x(t)

plot(n,x);

title('sinewave [f=1khz, fs=8khz]');

xlabel('sample number');

ylabel ('amplitude');

OUTPUT



%to generate sinc function

x=linspace(-5,5);

y=sinc(x);

subplot(1,2,1);

plot(x,y)xlabel('time');


title('sinc function');

subplot(1,2,2);

stem(x,y);

xlabel('time');


title('sinc function');

OUTPUT



exp -5) to perform addition and multiplication of unit

step and sinusoidal signal and sequence

%program for addition and multiplication of unit step signal

and sequence

n1=1:1:9;

s1=[1 2 3 4 5 6 2 3 1];

subplot(4,1,1)

stem(n1,s1)xlabel('n1')

title('input sequence')

ylabel('amplitube')

n2=-2:1:6;

s2=[1 1 1 0 2 3 1 1 0 ];

subplot(4,1,2)

stem(n2,s2)xlabel('n2')

title('second sequence')

ylabel('amplitube')

xlabel('n2')

s3=s1+s2;

subplot(4,1,3);

stem(n2,s3)title('summed sequence')

ylabel('amplitube')

xlabel('n2')

s4=s1.*s2;

subplot(4,1,4);

stem(n2,s4)



title('multiplication')

ylabel('amplitube')

xlabel('n2')

OUTPUT



%program for addition and multiplication of sinusoidal signal

and sequence

t=[0:0.01:1];

A=8;

f1=2;

s1=A*sin(2*pi*f1*t);

f2=2;


figuresubplot(4,1,1)

plot(t,s1)

title('1 hz sine wave')

ylabel('amplitude')

%plot the 4 hz sine wave

subplot(4,1,2)

plot(t,s2)title('2 hz sine wave')

ylabel('amplitude')

%plot the summed sine wave

subplot(4,1,3);

plot(t,s1+s2)

title('summed sine wave')

ylabel('amplitude')xlabel('time(s)')

xmult=s1.*s2;

subplot(4,1,4)

plot(xmult);

title('multiplication');



ylabel('amplitude')

xlabel('time(s)')

OUTPUT



exp -6)To perform addition and multiplication of ramp signal and

sequence

% To perform addition and multiplication of ramp signal and sequence

t = -20:20;

i=1;

for k=-20:20

if k>0

ramp1(i) = k;

elseramp1(i) = 0;

end

i = i+1;

end

subplot(2,2,1);

stem(t,ramp1);

xlabel('Time');

ylabel('Ramp signal 1');grid on;

t = -20:20;

i=1;

for k=-20:20

if k>0

ramp2(i) = k;

else

ramp2(i) = 0;end

i = i+1;

end

subplot(2,2,2);

stem(t,ramp2);

xlabel('Time');



ylabel('Ramp signal 2');

grid on;

x_addition=ramp1+ramp2;

subplot(2,2,3);

plot(t,x_addition);

grid on;

xlabel('Time');

ylabel('Added Signal');

x_multiplication=ramp1.*ramp2;

subplot(2,2,4);

plot(t,x_multiplication);

grid on;

xlabel('Time');

ylabel('Multiplied Signal');

OUTPUT



exp -7) to perform amplitude scaling for signal and sequence

% ampllitude scalling

t=[0:0.01:1];a=8;

f1=2;


subplot(3,1,1)

plot(s1);

xlabel('t');

ylabel('ampltude');title('input signal');

s2=2*s1;

subplot(3,1,2)

plot(s2);

xlabel('t');

ylabel('ampltude');

title('amplified input signal');s3=s1/2;

subplot(3,1,3)

plot(s3);

xlabel('t');

ylabel('ampltude');

title('atteniated input signal');



OUTPUT



exp-8) to generate complex valued signal and plot its magnitude,

phase, real and imaginary part in four separate subplots

%even and odd parts

close all;

clear all;

t=0:.005:4*pi;

x=sin(t)+cos(t) % x(t)=sint(t)+cos(t)

subplot(2,2,1)

plot(t,x)

xlabel('t');

ylabel('amplitude')

title('input signal')

y=sin(-t)+cos(-t) % y=x(-t)

subplot(2,2,2)

plot(t,y)

xlabel('t');

ylabel('ampitude')

title('input signal with t=-t')

z=x+y

subplot(2,2,3)

plot(t,z/2)

xlabel('t');

ylabel('amplitude')

title('even part of the signal')

p=x-y

subplot(2,2,4)

plot(t,p/2)



xlabel('t');

ylabel('amplitude')

title('odd part of the signal')

OUTPUT



exp-9) to perform linear convolution between signals and

sequences

%linear convolution

clc;

close all;

clear all;

x=input('enter input sequence');

h=input('enter impulse response');y=conv(x,h);

subplot(3,1,1);

stem(x);

xlabel('n');

ylabel('h(n)');

title('input signal');

subplot(3,1,2);stem(h);

xlabel('n');

ylabel('y(n)');

title('impulse response');

subplot(3,1,3);

stem(y);

xlabel('n');

ylabel('y(n)');

title('linear convolution');

disp('The resultant sighnal is');

disp(y)



OUTPUTenter input sequence1432

enter impulse response1021

The resultant sighnal is

1462072



exp-10) to find the Fourier transform of a given signal

and plotting its magnitude and phase spectrum

% fast Fourier transform (magnitude and phase plot)

clc;

close all;

X=[1,1,1,1,zeros(1,4)];

N=8;

X=fft(X,N);

magX=abs(X),phase=angle(X)*180/pi;

subplot(2,2,1);

plot(magX);

grid

xlabel('k')

ylabel('X(k)')

subplot(2,1,2)

plot(phase);

grid

xlabel('k')

ylabel('degrees')



OUTPUT



exp -11)to find auto correlation and cross correlation

between signals and sequence

%cross correlation

close all;

clear all;

x=input('enter input sequence');

h=input('enter impulse sequence');

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

xlabel('n');ylabel('x(n)');


subplot(3,1,2);

stem(h);

xlabel('n');

ylabel('h(n)');title('impulse signal');

y=xcorr(x,h);

subplot(3,1,3);

stem(y);

xlabel('n');

ylabel('y(n)');

disp('the resultant sigal is');disp(y);

title('correlation signal');



OUTPUT

enter input sequence12

enter impulse sequence3

the resultant sigal is

0

0

0

1440

0

0



%autocorrelation

clc;

close all;

clear all;x=[1,2,3,4,5];

y=[4,1,5,2,6];

subplot(3,1,1);

stem(x);

xlabel('n');

ylabel('x(n)');


subplot(3,1,2);

stem(y);

xlabel('n');

ylabel('y(n)');


z=xcorr(x,x);

subplot(3,1,3);

stem(z);

xlabel('n');

ylabel('z(n)');

title('resultant signal signal');



OUTPUT



exp -12) verification of linearity and time invariance properties of a

given continuous/discrete system

%LINEARITY PROPERTY

clc;

clear all;

close all;

n=0:40; a=2; b=1;x1=cos(2*pi*0.1*n);

x2=cos(2*pi*0.4*n);

x=a*x1+b*x2;

y=n.*x;

y1=n.*x1;

y2=n.*x2;

yt=a*y1+b*y2;d=y-yt;

d=round(d);

if d==0

disp('given system satisfies linearity properity');

else

disp('given system doesn’t satisfy linearity property');

endsubplot(3,1,1); stem(n,y); grid;

subplot(3,1,2); stem(n,yt); grid;

subplot(3,1,3); stem(n,d); grid;



OUTPUT

Given system satisfies linearity property



%FOR NON LINEAR SYSTEM

clc;

clear all;

close all;

n=0:40; a=2; b=-3;

x1=cos(2*pi*0.1*n);

x2=cos(2*pi*0.4*n);

x=a*x1+b*x2;

y=x.^2;

y1=x1.^2;

y2=x2.^2;

yt=a*y1+b*y2;

d=y-yt;

d=round(d);

if d==0

disp('given system satisfies linearity properity');else

disp('given system doesn’t satisfy linearity property');

end

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

subplot(3,1,2); stem(n,yt); grid;

subplot(3,1,3); stem(n,d); grid;



OUTPUT

given system satisfies doesn’t linearity property



exp -13) to perform waveform synthesis using Laplace

transform

% laplace transform programs

clc;close all;

clear all;

syms t w s;

f1=sin(w*t);

f2=sin(w*(t-1));

v1=laplace(f1);

v2=laplace(f2);disp('v1=')

pretty(v1);

disp('v2=')

pretty(v2);

OUTPUT



% INVERSE laplace transform programs

close all;

clear all;syms F s;

F=24/(s*(s+8));

iLaplace(F)

OUTPUT



exp -14) to perform image operations ;- read, resize,

rotate, and rgb to grayscale.

basicimageprocessing

% reading image...

A=imread('tanmay.jpg');

figure(1):imshow(A);

% resizing image....

B=imresize(A,[60,60]);

figure(2):imshow(B);

% color conversion..from rgb to grayscale image...

C=rgb2gray(A);

figure(3):imshow(C);

% rotating image....

D=imrotate(A,45);

figure(4):imshow(D);



Output

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