What are the frequencies when N in fft(x,N) is odd?

I know when N is even, fft(x,N) corresponds to frequencies 0,df,...,N/2*df,-(N/2-2)*df,...,-df.

What about if N is odd?

Answer 1

[Honglei Chen]

In general, you can do it as

f = (0:N-1)*fs/N

If you want to map it to negative frequencies

if N is even

f(N/2+1:end) = f(N/2+1:end)-fs % sample -fs/2

or

f(N/2+2:end) = f(N/2+2:end)-fs  % sample fs/2

if N is odd

f((N+1)/2+1:end) = f((N+1)/2+1:end)-fs

HTH

[Ray Lee]

why there are different two for even N?

[Honglei Chen]

-fs/2 and fs/2 are the same point due to periodicity. The difference is really just which one you want to display in your axis

[Ray Lee]

the output of fft is unique, but in the two formulae, the f axis is shifted by one point.

[Honglei Chen]

That's not true. Only one point is changed, from fs/2 to -fs/2 and because the result is periodic, they are indeed the same so you can mark it either way

[Eric]

To be clear, if you are using fftshift on your FFT data and N is even, use the first option (repeated here):

f(N/2+1:end) = f(N/2+1:end)-fs % sample -fs/2

Answer 2

[Michael scheinfeild]

if x is ampled at fs you can generate frequency vector use

freqvec=linspace(0,fs,N);

[Ray Lee]

I don't think so. The negative frequencies are missing.

[Honglei Chen]

This is incorrect. linspace always sample the last one, which you don't want.

[CHAN CHEN HUA]

@Honglei Chen Hi, can i know why last sample should not be taken into?