[Numpy-discussion] Spectral approximation/DFT

Magnus Lie Hetland magnus at hetland.org
Thu Jul 25 12:12:11 CDT 2002


Sorry to ask what is probably a really clueless question -- if there
are any obvious sources of information about this, I'd be happy to go
there and find this out for myself... :]

Anyway; I'm trying to produce a graph to illustrate a time sequence
indexing method, which relies on extracting the low-frequent Fourier
coefficients and indexing a vector consisting of those. The graph
should contain the original time sequence, and one reconstructed from
the Fourier coefficients. Since it is reconstructed from only the
low-frequent coefficients (perhaps 10-20 coefficients), it will look
wavy and sinus'y.

Now... I'm no expert in signal processing (or the specifics of FFT/DFT
etc.), and I can't seem to make the FFT module do exactly what I want

It seems that using fft(seq).real extracts the coefficients I'm after
(though I'm not sure whether the imaginary components ought to figure
in the equation somehow...)

But no matter how I use inverse_fft or inverse_real_fft it seems I
have to supply a number of coefficients equal to the sequence I want
to approximate -- otherwise there will be a huge offset between them.
Why is this so? Shouldn't the first coefficient take care of such an
offset? Perhaps inverse_fft isn't doing what I think it is?

If I haven't expressed myself clearly, I'd be happy to elaborate...

(For those who might be interested, the approach is described in the
paper found at http://citeseer.nj.nec.com/307308.html with a figure of
the type I'm trying to produce at page 5.)

Anyway, thanks for any help :)

Magnus Lie Hetland                                  The Anygui Project
http://hetland.org                                  http://anygui.org

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