Plotting DTFT in Matlab

I'm trying to create a DTFT function in Matlab for my assignment.

I'm using the built-in FFT function to compare my results and wager if my results are correct (I'm assuming the results should be the same just with different error margins), but the result I'm getting is entirely different and I'm not sure why.

Main code:

L = 1000;

fg = 1000;

fs = 100000;

T = 1/fs;

tmin = 0;

K = 1;

n = tmin:L;

t = n*T;

%Base function calculation

x = xdp1(K, fg, t);

%Fourier transform calculation

w = t;

%X = dtft(x, t);

%X = dtft2(x, w, n);

X = dtft3(x, w, n);

X_FFT = fft(x);

% Top plot

tiledlayout(3,1)

nexttile

plot(t, x)

ylim([min(x) max(x)])

xlim([0 max(t)])

title('Signal')

% Middle plot

nexttile

plot(t, abs(X));

title('DTFT')

% Bottom plot

nexttile

plot(t, abs(X_FFT))

ylim([min(abs(X_FFT)) max(abs(X_FFT))])

xlim([0 max(t)])

title('FFT')

Signal calc code (xdp1):

function x = xdp1(K, fg, t)

x = K * 2 * fg * sinc(2 * pi * fg * t);

end

DTFT calc code (dtft3):

function X = dtft3(x, w, n)

X = exp(-1i*w'*n) * x.';

end

My other attempts that minimized the Matlab exclusive syntax:

DTFT calc code (dtft2):

function X = dtft2(x, w, n)

for i=1:length(w)

X(i)=sum(x.*exp(-1i*w(i)*n));

end

end

DTFT calc code (dtft):

function X = dtft(x, w)

X = zeros(1, length(x));

for n=1:length(x)

X = X + x(n) * exp(-1i * w * n);

end

end

Result plot:

Answer 1

[Ishan]

Hi Tomasz,

I understand you are trying to cross verify your DTFT function. You can refer to the functions in the file exchange attached below

Digital Signal Processing -- Discrete-time Fourier Transform (DTFT) - File Exchange - MATLAB Central (mathworks.com)

Hope this helps out!