MATLAB program to find DFT and IDFT using matlab functions

Program Code

%DFT and IDFT using matlab functions
clc;
close all;
clear all;
x=input('Please enter the sequence x(n)=');
N=input('Please enter the length of the DFT N=');
X=fft(x,N);
n=0:length(x)-1;
subplot(311);
stem(n,x);
title('Input Sequence');
subplot(323);
n=0:length(X)-1;
stem(n,X);
disp('DFT of input sequence is ');
disp(X);
title('DFT');
subplot(324);
stem(n,abs(X));
title('Magnitude spectrum');
subplot(325);
stem(n,angle(X));
title('Phase spectrum');
xr=ifft(x,N);
subplot(326);
stem(n,abs(xr));
title('IDFT');
disp('IDFT of input sequence is ');
disp(xr);

Example of Output

Please enter the sequence x(n)=[1 2 3 4 5 6 7 8 9]
Please enter the length of the DFT N=6
DFT of input sequence is 
  Columns 1 through 4

  21.0000 + 0.0000i      -3.0000 + 5.1962i       -3.0000 + 1.7321i       -3.0000 + 0.0000i

  Columns 5 through 6

  -3.0000 - 1.7321i          -3.0000 - 5.1962i

IDFT of input sequence is 
  Columns 1 through 4

   3.5000 + 0.0000i       -0.5000 - 0.8660i         -0.5000 - 0.2887i       -0.5000 + 0.0000i

  Columns 5 through 6

  -0.5000 + 0.2887i         -0.5000 + 0.8660i

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MATLAB program to find IDFT without using MATLAB function

Program Code

%IDFT program without function
clc;
close all;
clear all;
X=input('Enter the sequence');
N=input('Enter the length of the IDFT');
len=length(X);
if N>len
    X=[X zeros(1,N-len)];
elseif N<len
    X=X(1:N);
end
i=sqrt(-1);
w=exp(-i*2*pi/N);
n=0:(N-1);
k=0:(N-1);
nk=n'*k;
W=w.^(-nk);
x=(X*W)/N;
disp(x);
subplot(211);
stem(k,abs(x));
title('Magnitude Plot');
xlabel('N');
ylabel('Amplitude');
grid on;
subplot(212);
stem(k,angle(x));
title('Phase Plot');
xlabel('N');
ylabel('Phase Angle');
grid on;

Example of Output

Enter the sequence     [24.0000       -2.3264 -13.6637i             3.0930 + 4.7651i        1.2334 - 6.2528i        1.2334 + 6.2528i 3.0930 - 4.7651i        -2.3264 +13.6637i]

Enter the length of the IDFT    4

6.1917 - 2.2247i         7.1913 + 2.0611i       5.8083 - 4.6072i   4.8087 + 4.7708i

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