Plotting DTFT of Finite Sum in MATLAB

[XcKyle93]

Homework Statement

x[n] = Ʃ c_k * δ(n-k), from k = -N to N. Plot the DTFT as a function of the number of terms N. This is a finite sum.

Homework Equations

The equation for the DTFT of a signal, which is Ʃ x[n] * e^{-j*2∏*∅*n}, from n = -∞ to +∞

The Attempt at a Solution

I have nothing... something like
N = 50;
ck = 1;


X = [];
phi = 1/(2*pi);

for n = -1000:1:1000
sum = 0;
for k = -N:1:N
sum = sum + dirac(n-k);
end
X = [X sum*exp(-1i*2*phi*n)];
end


n = -1000:1:1000;
plot(n, X);

But this is obviously wrong. I don't know how to compute the DTFT for a signal of a finite length like that, much less plot it using MATLAB!

 

[KataKoniK]

Thank you for your forum post. I understand your struggle with computing and plotting the DTFT for a finite sum. However, there are a few things that can help you in this task.

Firstly, it is important to note that the DTFT is a continuous function and can only be plotted using a continuous variable. In your attempt at a solution, you have used a discrete variable for n, which will not accurately represent the DTFT.

To compute the DTFT for a finite sum, you can use the following steps:

1. Define the values of N and ck.
2. Create a vector n that represents the continuous variable for the DTFT.
3. Use the equation for the DTFT to compute X for each value of n.
4. Plot n against X.

In MATLAB, you can use the "stem" function to plot a discrete signal. However, since the DTFT is a continuous function, it is better to use the "plot" function to plot n against X.

I have provided a sample code below, assuming N = 50 and ck = 1. I hope this helps in your understanding and plotting of the DTFT.

N = 50;
ck = 1;
n = -1000:0.1:1000; % use a smaller step size for a smoother plot
X = zeros(size(n));

for k = -N:N
X = X + ck*exp(-1i*2*pi*k*n);
end

plot(n, X);
xlabel('n');
ylabel('DTFT');
title('Plot of DTFT for finite sum');

Best of luck with your homework!