How can I find the value of Inverse DFT

I have dt signal $$x[n]={[6.29, 8.11,-7.46,8.26,2.64,-8.04,-4.43,0.93,-9.29]}$$

And I need to give the function value of:

1) sum of $$x[n] = \sum\limits_{k=0}^{N-1} X[k] \, e^{-j 3 \pi k/5}$$ from k=0 to 9

How can I find that

• hi. Your question is practically unreadable. Please fix that and explain why you haven't been able to simply apply the formula. Feb 21 '19 at 23:04

I don't know if I understand exactly what you mean, because your question is very unclear (you may need to edit it), but I will try to answer what you may need in your task.

For DFT you will need this equation:

$$X[k] = \sum\limits_{n=0}^{N-1} x[n] \, e^{-j 2 \pi nk/N}$$

where $$k = 0, 1, . . . , N − 1$$

But I guess you will be asking for IDFT more, so first you need to understand how IDFT works. I will try to explain this in my picture: So the formula will look like this:

$$x[n] = \frac{1}{N} \sum\limits_{k=0}^{N-1} X[k] \, e^{j 2 \pi nk/N}$$

where $$n = 0, 1, . . . , N − 1$$

Note that here, x[n] will be our complex time series, and X[k] is complex frequencies.

Now, we can get your sum, thanks to a simple code:

x = [6.29 8.11 -7.46 8.26 2.64 -8.04 -4.43 0.93 -9.15 9.29];
XF = fft(x);
k =  0:9;
YF = exp(-i*3*pi*k/5).*XF;
output = [sum(YF)];
disp(output)

And, as we can see, the sum equals 9.3.