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Adapted a mail from Mark about some design and add it as documentation for

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the FFT module.
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Thomas Capricelli 2009-11-30 16:21:21 +01:00
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unsupported/Eigen/FFT
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@ -44,11 +44,42 @@
* The build-in implementation is based on kissfft. It is a small, free, and
* reasonably efficient default.
*
* Frontends are
* There are currently two frontends:
*
* - fftw (http://www.fftw.org) : faster, GPL -- incompatible with Eigen in LGPL form, bigger code size.
* - MLK (http://en.wikipedia.org/wiki/Math_Kernel_Library) : fastest, commercial -- may be incompatible with Eigen in GPL form
* - MLK (http://en.wikipedia.org/wiki/Math_Kernel_Library) : fastest, commercial -- may be incompatible with Eigen in GPL form.
*
* \section FFTDesign Design
*
* The following design decisions were made concerning scaling and
* half-spectrum for real FFT.
*
* The intent is to facilitate generic programming and ease migrating code
* from Matlab/octave.
* We think the default behavior of Eigen/FFT should favor correctness and
* generality over speed. Of course, the caller should be able to "opt-out" from this
* behavior and get the speed increase if they want it.
*
* 1) %Scaling:
* Other libraries (FFTW,IMKL,KISSFFT) do not perform scaling, so there
* is a constant gain incurred after the forward&inverse transforms , so
* IFFT(FFT(x)) = Kx; this is done to avoid a vector-by-value multiply.
* The downside is that algorithms that worked correctly in Matlab/octave
* don't behave the same way once implemented in C++.
*
* How Eigen/FFT differs: invertible scaling is performed so IFFT( FFT(x) ) = x.
*
* 2) Real FFT half-spectrum
* Other libraries use only half the frequency spectrum (plus one extra
* sample for the Nyquist bin) for a real FFT, the other half is the
* conjugate-symmetric of the first half. This saves them a copy and some
* memory. The downside is the caller needs to have special logic for the
* number of bins in complex vs real.
*
* How Eigen/FFT differs: The full spectrum is returned from the forward
* transform. This facilitates generic template programming by obviating
* separate specializations for real vs complex. On the inverse
* transform, only half the spectrum is actually used if the output type is real.
*/