Your DSP Lab Codes.

%% Generation of continuous time signal
clc; clear all;
t = 0:0.0005:1;
a = 10;
f = 13;
xa = a*sin(2*pi*f*t);
subplot(2,1,1); plot(t,xa);grid
xlabel('Time, msec'); ylabel('Amplitude'); title('Continuous-time signal x_{a}(t)');;
axis([0 1 -11 11])

clear all;
a = 10;
f = 13;
T = 0.01;
n = 0:T:1;
xs = a*sin(2*pi*f*n);
k = 0:length(n)-1;
stem(k,xs);
grid
xlabel('Time index n');
ylabel('Amplitude');
title('Discrete-time signal x[n]');
axis([0 (length(n)-1) -10.2 10.2])

% Generations of Elementary Sequences  
clc; clear all; close all;  
t = -3:1:3;  
y = [zeros(1,3),ones(1,1),zeros(1,3)];  
subplot(2,2,1);stem(t,y);  
ylabel('Amplitude  >'); xlabel('(a)n  >'); title('Unit Impulse Signal');  

% program for generation of unit step of sequence [u(n)- u(n)-N]  
t  = -4:1:4;  
y1 = ones(1,9);  
subplot(2,2,2);stem(t,y1);  
ylabel('Amplitude  >'); xlabel('(b)n  >'); title('Unit step');  

% program for generation of ramp signal  
n1 = input('Enter the value for end of the seqeuence '); %n1 = <any value>7 %  
x = 0:n1;  
subplot(2,2,3);stem(x,x);  
ylabel('Amplitude  >'); xlabel('(c)n  >'); title('Ramp sequence');  

% program for generation of exponential signal  
n2 = input('Enter the length of exponential seqeuence ');     %n2 = <any value>7   
t  = 0:n2;  
a  = input('Enter the Amplitude');     %a=1   
y2 = exp(a*t);  
subplot(2,2,4); plot(t,y2);  
ylabel('Amplitude  >'); xlabel('(d)n  >'); title('Exponential sequence');  

disp('Unit impulse signal');y  
disp('Unit step signal'); y1 
disp('Unit Ramp signal'); x 
disp('Exponential signal');y2

% Summation and Subtraction Processes
clc; clear all; close all;

n1 = -2:1;
x = input('ENTER THE FIRST SEQUENCE X: ');

n2 = 0:3;
y = input('ENTER THE SECOND SEQUENCE Y: ');

subplot(2,2,1);
stem(n1,x); grid on;
xlabel('time');
ylabel('amplitude');
title('FIRST SEQUENCE');
axis([-4 4 -5 5]);

subplot(2,2,2);
stem(n2,y); grid on;
xlabel('time');
ylabel('amplitude');
title('SECOND SEQUENCE');
axis([-4 4 -5 5]);

% Finding the duration of output signal
n3 = min(min(n1),min(n2)):max(max(n1),max(n2));

s1 = zeros(1,length(n3));
s2 = zeros(1,length(n3));

s1((n3>=min(n1)) & (n3<=max(n1))) = x;
s2((n3>=min(n2)) & (n3<=max(n2))) = y;

% Summation
summ = s1+s2;
disp('Summation Results')
disp(summ)

subplot(2,2,3);
stem(n3,summ); grid on;
xlabel('time');
ylabel('amplitude');
title('SUMMATION');
axis([-4 4 -5 5]);

% Subtraction
sub = s1-s2;
disp('Subtraction Results')
disp(sub)

subplot(2,2,4);
stem(n3,sub); grid on;
xlabel('time');
ylabel('amplitude');
title('SUBTRACTION');
axis([-4 4 -5 5]);

clc; clear all; close all;
x =input('ENTER THE SEQUENCE x(n):');
n1=input('Enter the amount to be delayed = ');
n2=input('Enter the amount to be advanced = ');
n = -2:2;
subplot(4,1,1); stem(n,x); grid
title('Signal x(n)');
axis([min(n)-n2 max(n)+n1 -5 5]);
% Delay
m=n+n1;
subplot(4,1,2); stem(m,x); grid
title('Delayed signal x(n-n1)');
axis([min(n)-n2 max(n)+n1 -5 5]);
% Advance
t=n-n2;
subplot(4,1,3); stem(t,x); grid
title('Advanced signal x(n+n2)');
axis([min(n)-n2 max(n)+n1 -5 5]);
%Folding or reversing:
c = fliplr(x);
y = fliplr(-n);
disp('FOLDED SEQUENCE')
disp(c)
subplot(4,1,4); stem(y,c); grid
title('Folded Signal x(-n)');
axis([min(n)-n2 max(n)+n1 -5 5]);

clc; clear all; close all;
x=input('enter the 1st sequence ');
h=input('enter the 2nd sequence ');
%% Linear Convolution
y = conv(x,h);
% Plot Linear Convolution
l = length(y);
figure; subplot(3,1,1); stem(x);xlim([0 l])
ylabel('Amplitude --.'); xlabel('(a) n --.'); title('first sequence');
subplot(3,1,2); stem(h);xlim([0 l])
ylabel('Amplitude --.'); xlabel('(b) n --.'); title('Second sequence');
subplot(3,1,3); stem(y); xlim([0 l])
ylabel('Amplitude --.'); xlabel('(c) n --.'); title('Convoluted sequence');
disp('The resultant signal is'); y
%% Circular Convolution
% Zero Padding Linear Convolution
nx = length(x);
nh = length(h);
% N = max(nx,nh); % N = nx+nh-1; %Choice #1
%Choice #2
N = input('enter the length of the circular CONV '); %Choice #3
%
xpd = [x zeros(1,(N-nx))];
hpd = [h zeros(1,(N-nh))];
for i = 1:N
    k = i;
    for j = 1:nh
        H(i,j)=xpd(k)*hpd(j);
        k = k-1;
        if k == 0
            k = N;
        end
    end
end
yc=zeros(1,N);
M=H';
for j = 1:N
    for i = 1:nh
        yc(j)=M(i,j)+yc(j);
    end
end
disp('The output sequence is yc(n)='); yc
%Plot Cicular Convolution
lc = length(yc);
figure;
subplot(3,1,1); stem(xpd);xlim([0 lc])
ylabel('Amplitude --.'); xlabel('(a) n --.'); title('first sequence');
subplot(3,1,2); stem(hpd);xlim([0 lc])
ylabel('Amplitude --.'); xlabel('(b) n --.'); title('Second sequence');
subplot(3,1,3); stem(yc); xlim([0 lc])
ylabel('Amplitude --.'); xlabel('(c) n --.'); title('Circular Convolution');

clc; clear all; close all;
tfinal = 0.05;
t = 0:0.00005:tfinal;
f = input('Enter the analogy frequency f = ');
xt = cos(2*pi*f*t);
%Under sampling plot
fs1 = 1.3*f;
n1 = 0:1/fs1:tfinal;
xn = cos(2*pi*f*n1);
subplot(3,1,1); plot(t,xt,'b',n1,xn,'r*-');
title('under sampling'); xlabel('time'); ylabel('amplitude');
%Nyquist plot
fs2=2*f;
n2 = 0:1/fs2:tfinal;
xn = cos(2*pi*f*n2);
subplot(3,1,2); plot(t,xt,'b',n2,xn,'r*-');
title('nyquist sampling'); xlabel('time'); ylabel('amplitude');
%Over sampling plot
fs3 = 5*f;
n3 = 0:1/fs3:tfinal;
xn = cos(2*pi*f*n3);
subplot(3,1,3); plot(t,xt,'b',n3,xn,'r*-');
title('over sampling'); xlabel('time'); ylabel('amplitude');

clc; clear all; close all;
f1 = input('Enter the first sine wave frequency f1 = ');
f2 = input('Enter the second sine wave frequency f2 = ');
fn = 2*max(f1,f2);
fs = 0.5*fn;
t = [0:1/fs:0.1];
x = cos(2*pi*f1*t)+cos(2*pi*f2*t);
xk = fft(x);
f = [0:length(xk)-1]*fs/length(xk);
figure, plot(f,abs(xk));
xlabel('frequency'); ylabel('amplitude'); title('Under Sampling');
grid;
fs = fn;
t = 0:1/fs:0.1;
x = cos(2*pi*f1*t)+cos(2*pi*f2*t);
xk = fft(x);
f = [0:length(xk)-1]*fs/length(xk);
figure; plot(f,abs(xk));
xlabel('frequency');ylabel('amplitude');title('Nyquist Rate Sampling');
grid;
fs = 5*fn;
t = 0:1/fs:0.1;
x = cos(2*pi*f1*t)+cos(2*pi*f2*t);
xk = fft(x);
f = [0:length(xk)-1]*fs/length(xk);
figure; plot(f,abs(xk));
xlabel('freq'); ylabel('Amplitude');title('Over Sampling');
grid;