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.
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.