Given the sequences x1 = [1 4 5], x2 = [1 5 7 9 6 11] Find the linear convolutio

Question

Given the sequences x1 = [1 4 5], x2 = [1 5 7 9 6 11] Find the linear convolution by manual synthetic multiplication then check your result using Matlab's conv() function Pad each sequence with zeros so that each is a length of 8. call them x1p and x2p. Compute x1p[n] * x2p[n] using linear convolution by Matlab, i.e., conv() Next take the DFT/fft of each sequence X1P = fft(x1p) and do a point by point multiplication of the terms to get XX. Then take the inverse DFT/FFF xx = ifft(XX) and compare to the linear convolution result. Write you code with sufficient documentation and publish it as a pdf

Explanation / Answer

Matlab Script:

clc;
clear all;
x1 = [1 4 5];
x2 = [1 5 7 9 6 11];
xx1 = conv(x1,x2);%taking linear convolution
x1p = [1 4 5 zeros(1,5)];%padding with zeros to make length 8
x2p = [1 5 7 9 6 11 0 0];%padding with zeros to make length 8
X1P = fft(x1p);%taking fft of x1p
X2P = fft(x2p);%taking fft of x2p
XX = X1P.*X2P;%taking point by point multipliction
xx = ifft(XX);%taking ifft of XX

command window output:

>> xx

xx =

1 9 32 62 77 80 74 55

>> xx1

xx1 =

1 9 32 62 77 80 74 55

>>

both of them are same

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