# DFT scaling property

Discussion in 'Math' started by Georacer, Apr 2, 2013.

1. ### Georacer Thread Starter Moderator

Nov 25, 2009
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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.

Last edited: Apr 2, 2013
2. ### t06afre AAC Fanatic!

May 11, 2009
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Frequency or amplitude?

3. ### Georacer Thread Starter Moderator

Nov 25, 2009
5,151
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The starting signal x[n] is real.
X[k] is the complex-valued DFT.

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

4. ### Georacer Thread Starter Moderator

Nov 25, 2009
5,151
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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.

May 11, 2009
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6. ### Georacer Thread Starter Moderator

Nov 25, 2009
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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.