Student Seminar Report & Project Report With Presentation (PPT,PDF,DOC,ZIP)

Procedure:-
1) Find the length of the first sequence x[n]=x_length
2) Find the length of the second sequence h[n]=h_length
3) Estimate the number of samples in the result of linear convolution of x[n] &h[n]=Y_length
4) If X_length <Y_length , pad enough number of zeros to x[n], so that the number of samples in the modified x[n]=Y_length
5) If h_length <Y_length ,pad enough number of zeros to h[n], so that the number of samples in the modified h[n]=Y_length
6) Take DFT for modified x[n]=x(k)
7) Take DFT for modified h[n]=H(k)
8) Compute Y(K)=X(K)*H(K)
9) Compute y(n)=IDFT(Y(k))
10) Verify if y[n]=conv(x,h)

MATLAB program for linear convolution using DFT and IDFT

Code:
clear 

clc

close all

% FIRST SEQUENCE X1

x1 = [1 1 1 1];

nx1 = 0:length(x1)-1;

n1 = length(x1);

subplot(3,1,1);

stem(nx1,x1);

xlabel('n-->');

ylabel('x1-->');

title('First Sequence');

grid on;

% SECOND SEQUENCE X2

x2 = [1 1 1 1];

nx2 = 0:length(x2)-1;

n2 = length(x2);

subplot(3,1,2);

stem(nx2,x2);

xlabel('n-->');

ylabel('x2-->');

title('Second Sequence');

grid on;

N = n1+n2-1;

% IF N > length(x1) or length(x2) ZERO PAD

newx1 = [x1,zeros(1,N-n1)];

newx2 = [x2,zeros(1,N-n2)];

% TAKE DFT OF FIRST SEQUENCE

x1dft = fft(newx1);

% TAKE DFT OF SECOND SEQUENCE

x2dft = fft(newx2);

% MULTIPLY THE TWO DFTS

ydft = x1dft .* x2dft

% TAKE IDFT OF THE PRODUCT OF TWO DFTS

disp('Response obtained by DFTs')

y = ifft(ydft)

n = 0:length(y)-1;

subplot(3,1,3);

stem(n,y);

xlabel('n-->');

ylabel('x2-->');

title('Linearly convoluted Sequence');

grid on;

% VERIFICATION WITH DIRECT CONVOLUTION

disp('Response obtained by DFTs')

Ydirect = conv(x1,x2)

RESULT:- LINEAR CONVOLUTION USING DFT AND IDFT

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