Please help me with this DFT problem Consider the 8point seq

Please help me with this DFT problem

Consider the 8-point sequence: x[n] = {4,2,1,3,4,3,1, 2}. (i) Compute the 8-point DFT X[k] of x[n]. (ii) Compute the 8-point DFT using the decimation-in-time (DIT) FFT algorithm. Show the intermediate values at the output of every butterfly configuration in each stage of the DIT algorithm. (iii) Compute the reduction in complexity achieved by using the FFT algorithm compared to direct computation of the DFT.

Solution

clear all;

close all;

%x=[4 2 1 3 4 3 1 2]

x=input(\'enter the input sequence\');

n=input(\'enter the lenth of DFT\');

subplot(4,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'input signal\');

y=fft(x,n);

subplot(4,1,2);

stem(y);

xlabel(\'frequency\');

ylabel(\'amplitude\');

title(\'discrete fourier transform\');

z=abs(y);

subplot(4,1,3);

stem(z);

xlabel(\'frequency\');

ylabel(\'magnitude\');

u=angle(y);

subplot(4,1,4);

stem(u);

xlabel(\'frequency\');

ylabel(\'phase plot\');

:

enter the input sequence[1 2 3 4]

enter the lenth of DFT16