5. To find N point DFT and plot its magnitude and phase spectra. To find N point DFT and plot its magnitude and phase spectra.

 Code:

//To calculate DFT of the sequence:

clear all;

clc;

close;

x=input(" Input sequence x :- ")

nl=input("length of input sequence :- ")

if length(x)<nl then

x=[x zeros(1,nl-length(x))]

end

n=0:nl-1;

k=0:nl-1;

//dft

Xdft= x*exp(-%i*((2*%pi)/nl)* k'*n); //dft formula

Xdft1=fft(x); // direct Command

//Idft

Xidft = (Xdft*exp(%i*((2*%pi)/nl)* k'*n))/nl; //idft formula

Xidft1=ifft(X); /// direct command

figure(1);

//input sequence

subplot(2,2,1);

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(n,x)

ylabel("x[n]");

xlabel("n");

title("Input sequence");

//DFT sequence 'Xdft'

subplot(2,2,2);

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(k,Xdft)

ylabel("Y[k]");

xlabel("k");

title("DFT sequence");

//IDFT sequence 'Xidft'

subplot(2,2,3);

a=gca();

a.x_location="origin";

a.y_location="origin";

plot2d3(n,Xidft)

ylabel("X[n]");

xlabel("n");

title("IDFT sequence");

disp("Input Sequence x")

disp (x');

disp("DFT Sequence Xdft")

disp ( round(Xdft)');

disp("IDFT Sequence Xidft")

disp ( round(Xidft)');