Matlab Code to obtain DFT and plot its magnitude and phase response

Matlab Code:- 

clc;

clear all;

close all;

x=input('Enter the sequence: ');

N=length(x);

Wn=exp((-j*2*pi)/N);%Twiddle factor

fprintf('Twiddle Factor=%f+j(%f)\n',real(Wn),imag(Wn));

disp('Magnitude and phase of Twiddle Factor:');

    fprintf('|Wn|=%f    ',Wn);

    fprintf('angle Wn=%f\n', angle(Wn));

 fprintf('\n'); 

for k=1:N

    X(k)=0;

end

%Calculation of DFT

for k=1:N

    for n=1:N

        X(k)=X(k)+(x(n)*Wn^((k-1)*(n-1)));

    end

end

%Printing the DFT

fprintf('DFT of x(n) is:\n');

disp(X);

fprintf('\n');

fprintf('X(k)\tMagnitude\tPhase\n\n');

for k=1:N

    fprintf('X(%d)\t%f\t%f\n',k-1,X(k),angle(X(k)));

end

%To plot the magnitude and phase of the DFT

subplot(1,2,1);

stem(X,'linewidth',1.5);

xlabel('k--->');

ylabel('magnitude--->');

title('Magnitude Response');

grid on;

subplot(1,2,2);

stem(angle(X),'linewidth',1.5);

xlabel('k--->');

ylabel('phase--->');

title('Phase Response');

grid on;

Output:-

Enter the sequence: [0.5 0 0.5 0]

Twiddle Factor=0.000000+j(-1.000000)

Magnitude and phase of Twiddle Factor:

|Wn|=0.000000    angle Wn=-1.570796

DFT of x(n) is:

   1.0000 + 0.0000i   0.0000 - 0.0000i   1.0000 + 0.0000i   0.0000 - 0.0000i

X(k) Magnitude Phase

X(0) 1.000000    0.000000

X(1) 0.000000    -1.570796

X(2) 1.000000     0.000000

X(3) 0.000000    -1.570796