Hello everybody,

In the context of DFT, I am given an 8-point signal x[n] with the 8-point DFT of X[k].

What is the IDFT of the sequence X[2k], for k=0-3?
I 've been trying to find a formal answer specifically for the DFT all day but to no avail.

Can you point me to a resource or provide an answer? A proof would be even better.

Thanks in advance.

 

Frequency or amplitude?

 

The starting signal x[n] is real.
X[k] is the complex-valued DFT.

In short, I 'm interested in general, complex quantities.

 

I got the answer after all.

When downsampling the frequency by two, the time signal is wrapped in a new periodic signal of half the period and aliasing happens.

Thus, if P[k]=X[2k], k=0,...,3 then
p[n]=[x[0]+x[4] x[1]+x[5] x[2]+x[6] x[3]+x[7]]

It dawned on me after reading the problem solution for two days.

 

Sounds to me that you are talking about the Nyquist frequency. Remember that the Nyquist frequency is kind of a theoretical limit. If you want a good reproduction of your sampled signal. I would in practical designs recommend sampling with at least with a frequency 10 times higher than the signal frequency of interest
http://en.wikipedia.org/wiki/Nyquist_frequency
http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

 

This was a uni course theoretical question, so there was no room for experimentation.

The question was:
You have x[n]=[ 2 -1 1 0 3 -2 3 -3]
If X[k] is the 8-point DFT of x[n], what is r[n], if R[k]=|X[2k]|^2?

As you can see, it was a bit more complex and broad than my original question.