Coverage for local/lib/python2.7/site-packages/sage/gsl/dft.py : 0%

r""" 

Discrete Fourier Transforms 

This file contains functions useful for computing discrete Fourier 

transforms and probability distribution functions for discrete random 

variables for sequences of elements of `\QQ` or `\CC`, indexed by a 

``range(N)``, `\ZZ / N \ZZ`, an abelian group, the conjugacy classes 

of a permutation group, or the conjugacy classes of a matrix group. 

This file implements: 

- :meth:`__eq__` 

- :meth:`__mul__` (for right multiplication by a scalar) 

- plotting, printing -- :meth:`IndexedSequence.plot`, 

:meth:`IndexedSequence.plot_histogram`, :meth:`_repr_`, :meth:`__str__` 

- dft -- computes the discrete Fourier transform for the following cases: 

* a sequence (over `\QQ` or :class:`CyclotomicField`) indexed by ``range(N)`` 

or `\ZZ / N \ZZ` 

* a sequence (as above) indexed by a finite abelian group 

* a sequence (as above) indexed by a complete set of representatives of 

the conjugacy classes of a finite permutation group 

* a sequence (as above) indexed by a complete set of representatives of 

the conjugacy classes of a finite matrix group 

- idft -- computes the discrete Fourier transform for the following cases: 

* a sequence (over `\QQ` or CyclotomicField) indexed by ``range(N)`` or 

`\ZZ / N \ZZ` 

- dct, dst (for discrete Fourier/Cosine/Sine transform) 

- convolution (in :meth:`IndexedSequence.convolution` and 

:meth:`IndexedSequence.convolution_periodic`) 

- fft, ifft -- (fast Fourier transforms) wrapping GSL's 

``gsl_fft_complex_forward()``, ``gsl_fft_complex_inverse()``, 

using William Stein's :func:`FastFourierTransform` 

- dwt, idwt -- (fast wavelet transforms) wrapping GSL's ``gsl_dwt_forward()``, 

``gsl_dwt_backward()`` using Joshua Kantor's :func:`WaveletTransform` class. 

Allows for wavelets of type: 

* "haar" 

* "daubechies" 

* "daubechies_centered" 

* "haar_centered" 

* "bspline" 

* "bspline_centered" 

.. TODO:: 

- "filtered" DFTs 

- more idfts 

- more examples for probability, stats, theory of FTs 

AUTHORS: 

- David Joyner (2006-10) 

- William Stein (2006-11) -- fix many bugs 

""" 

########################################################################## 

# Copyright (C) 2006 David Joyner <wdjoyner@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL): 

# 

# http://www.gnu.org/licenses/ 

########################################################################## 

from sage.misc.superseded import deprecation 

deprecation(9084, "the module sage.gsl.dft has moved to sage.calculus.transforms.dft") 

from sage.calculus.transforms.dft import *