For each of the following 10point DFTs determine a formula t

For each of the following 10-point DFTs, determine a formula the 10-point IDFT. Use MATLAB to check your work numerically. X_a[k] = { 1 k=0 0 k = 1, 2,...,9 Xb[k] = 1 for k = 0,1, 2,...,9 X_c[k] = { 1 k = 3,7 0 k = 0,1, 2, 3,4,5,6,8,9 xd[k] = cos(27 pi k/5) for k = 0,1, 2,...,9

Solution

clear all;

close all;

%x=[1 2 3 4]

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\');