.. -*- rest -*-

================================================
  fftpack - Discrete Fourier Transform package
================================================

:Author: Pearu Peterson <pearu@cens.ioc.ee>
:Last changed: $Date$
:Revision: $Revision$
:Discussions to: scipy-dev@scipy.org

Installation
============

To build fftpack, you'll need F2PY version 2.23.190-1367 or higher.

Run

::

  python setup.py install

Testing
=======

Run

::

  python -c "import scipy.fftpack; scipy.fftpack.test()"

or from python

>>> import scipy.fftpack
>>> scipy.fftpack.test(10)


Differences between fftpack and FFT from Numeric
================================================

* Functions rfft and irfft accept and return only real sequences. So,
  the corresponding functions real_fft, inverse_real_fft from FFT are
  not equivalent with rfft and irfft. The difference is in the storage
  of data, see the definitions of corresponding functions for details.

* PROPOSAL: When calling ifft with forced truncation or zero-padding
  then I would like to propose that the corresponding action is
  applied to the middle of data. For example, ifft([1,2,3,4,5,6],n=8)
  is equivalent to ifft([1,2,3,4,0,0,5,6]), that is, the Fourier terms
  with higher frequencies and zero coefficients are introduced. In the
  Numeric.FFT case, the example above would be equivalent to
  ifft([1,2,3,4,5,6,0,0],n=8), which would mean that Fourier
  coefficients [5,6] become the coefficients of higher frequency terms
  and the original terms are zerod.

  Note that this proposal is **not implemented** because it needs to
  be discussed. For instance, Matlab uses the same convention as FFT
  and this change would be confusing for Matlab users.  On the other
  hand, FFT or Matlab's conventions change the spectrum of the
  original signal and I don't see any sense in this behaviour (if you
  don't agree then please provide an example). Namely, one of the
  applications of the argument n would be to compose a new signal with
  a more dense or sparse grid than the original one by using

  ::

    new_signal = ifft(fft(signal),n)

  Note that the new_signal would have the same Fourier spectrum as
  original signal. With Matlab/FFT convention this is not true.  Any
  thoughts?


Nyquist mode
============

Pseudo-differential and differential operators of odd order assume
that the Nyquist mode is zero that reduces the amplification of
numerical noise from the aliasing effect.

To do
=====

basic.py
  - Optimize ``fftn()`` for real input.
  - Implement ``rfftn()`` and ``irfftn()``.
  - Implement discrete cosine/sine transforms
pseudo_diffs.py
  - Optimize functions for complex input.
src/convolve.c
  - See if convolve could use convolution function from DJBFFT.

If you have any comments, please send them to scipy-dev@scipy.org.