Matlab Discrete Time Fourier Transform Algorithm

Question

Currently in a digital signal processing class, but need help reproducing the results of this code without using symbolic math in Matlab but rather using nested for loops to generate the values of X as a function of omega.

Symbolic Solution

This is what I have so far, using various matlab ideas for DTFT:

N=8;
figure
upper = pi;
lower = -pi;
bw = 1000;

omega = linspace(-pi,pi,1000);

for k=0:bw
    for n=0:N-1
         Y = X(k+1) + x(n+1)*exp(-j*2*pi*n*k/N) ;
    end
end

Please describe the problem you need help with. What result do you see, what is the result you would expect? Any idea why these two sets of results might differ? — Mouse On Mars

Unknown Unknown · Accepted Answer · 2019-04-06T17:37:57

The key is to focus on this part of the symbolic expression

%X is the sum of all 8 functions 0 to 7
X = f2(1) + f2(2) + f2(3) + f2(4) + f2(5) + f2(6) + f2(7) + f2(8)

And try to write your own code from that.


clear; clc;
figure

upper = pi
lower = -pi
bw = 1000

%w is in 1x1000
w =linspace(lower, upper, bw)

N=8

X=zeros(1, 1000)

for k=0:N

    f2=exp(-j*w*k);

    X = X + f2;

end

f4=X

subplot(2,1,1)

plot(linspace(lower, upper, bw), abs(f4), 'b');

Since I know that the we're looking for the sum of all 8 functions for n=1:8, I can achieve that in one line of code, as here

X = X + f2;

where here, the functions are contained in the vector f2,

f2=exp(-j*w*k);

This gets you the same result as the subplot for the reference code.

Matlab Discrete Time Fourier Transform Algorithm

1 Answers