real input to the dft
hello I got something like.
Well, for an 8-point DFT the last three
DFT samples (m=5, m=6, & m=7) are the
conjugates of the m=3, m=2, & m=1 DFT samples,
respectively. So what we say is:
The last three samples of an 8-pt DFT
give us *NO* new information about the
DFT's spectrum. (For an 8-point DFT, the
m=4 DFT sample is independent.) In fact,
once we have computed the first (N/2)+1 = 5
DFT samples, we don't need to compute the
last (N/2)-1 DFT samples.
Of course, that is only true for real-valued
input samples applied to the DFT, *AND* if the
DFT length, N, is an even number.
If N happens to be an odd number, then only the
first (N+1)/2 samples of the DFT are independent.
For example, with a 9-point DFT only the first
five DFT samples are independent.