The objective of this home work is to use Matlab to find Fourier Series Coeffici

Question

The objective of this home work is to use Matlab to find Fourier Series Coefficients for a given signal and then to use inverse Fourier Series Transform to recover the signal in time domain from the Fourier Coefficients. Follow the Example 3.19.2 on page 315 of the text book to find the Fourier Coefficient for the following signal. You will use the function fft to accomplish this.

Then use the function ifft to reconstruct the original signal from the Fourier Coefficients.

2. Use Matlab and find the Fourier Coefficients for the following signals.

                                                                                                         5pts

3a. Use the function ifft to determine the signal in the time domain for the following Fourier Coefficients.

b.

Does your result agree with the paper and pencil method you used to solve these problems?

Explanation / Answer

%x[n]=1+sin(n*pi/12 + 3*pi/8); %x(n)=cos(6/17*pi+pi/3); n=linspace(0,0.1,2*pi); x=cos((6/17)*pi +pi/3); plot(n,x);

% to write a program in matlab to perform auto correlation using DFT.

clear all;

close all;

clc;

x1=input('enter the first sequence');

x2=fliplr(x1);

l=length(x1);

x1=fft(x1);

x2=fft(x2);

f=x1.*x2;

j=ifft(f);

subplot(2,2,1);

stem(x1);

xlabel('input sequence');

ylabel('amplitude');

title('input sequence');

subplot(2,2,2);

stem(j);

xlabel('time');

ylabel('amplitude');

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