Re: Strange FFT Behavior in MATLAB

When analyzing (real) time series data, the complex
frequency spectrum is symmetric in the real part and
anti-symmetric in the imaginary part.

Way back in Matlab 3, when memory and performance were at a
premium, I formulated MEX files that used this symmetry to
reduce the data size.

It is possible to arrange a real time series into a complex
series of half the length and post process the fft output to
get the spectrum. Or the other way around - arranging half
the spectrum into a real series. For lengths of a power of
2, Matlab 3 used a fast Cooley Tukey algorithm which was
most efficient going from real to complex.

For even lengths that are not a power of 2, Matlab 3 only
used a complex FFT. In those cases, I took the real series
(either time series or half the spectrum), and arranged it
as a complex series of half the length. Again, I could take
half a frequency spectrum and rearrange it as a real series
then rearrange it again as a complex series of half the length.

It sounds more complicated than it was and it ran several
times faster.
.

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