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Warped FFT

DSP related issues, mathematics, processing and techniques

Warped FFT

Postby juha_tp » Wed Sep 09, 2020 11:39 am

Paper: ... e58600.pdf

Hmm... how can it be done in this code:

Code: Select all
% obtaining impulse response using cepstral processing
h = log(R);   % R^(k)  (R=magnitude squared response)
h = ifft(h);  % complex spectrum r^(n)
h = fft(h);   % R^mn(k)
h = exp(h);   % Rmn
h = ifft(h);  % h(n)
h = real(h);  % IR

which maybe is the culprit for some weird phenomenon in filter response (depending on filter type, affects in both ends of frequency spectrum) ... .

I would gladly like to try if WFFT could help in this issue. Can it be done ... ?
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Re: Warped FFT

Postby martinvicanek » Thu Sep 10, 2020 10:05 am

Warped FFT can be done, however it requires to run N allpass filters to warp the input data. That preprocessing spoils the FFT performance. You might just as well use Goertzel's algorithm for N log-spaced frequencies. ;)
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Re: Warped FFT

Postby juha_tp » Thu Sep 10, 2020 10:47 am

actually, low performance would not be an issue since code listing in my post is part of a filter generation process (MIM/PIM method) which can be slow anyway.
I'll check that Goertzel algorithm later.

There's also some method called LFT (Logarithmic Fourier Transform) (PDF file link) I'm interested on but, dunno if it could be used... . Any thoughts?
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Re: Warped FFT

Postby juha_tp » Fri Sep 18, 2020 6:58 am

If I have understood it right, LFT is implemented in python library "empymod" as FFTLog .... I could not find good examples for to test it in audio application so, have to ask if someone of you have already tried if LFT/iLFT works for audio field applications (impulse response using cepstral processing as for an example) and what changes are needed to do for data compared to FFT/iFFT usage and is this all possible to port into FS?
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