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"""
==================================================
Discrete Fourier transforms (:mod:`scipy.fftpack`)
==================================================
Fast Fourier Transforms (FFTs)
==============================
.. autosummary::
:toctree: generated/
fft - Fast (discrete) Fourier Transform (FFT)
ifft - Inverse FFT
fft2 - Two dimensional FFT
ifft2 - Two dimensional inverse FFT
fftn - n-dimensional FFT
ifftn - n-dimensional inverse FFT
rfft - FFT of strictly real-valued sequence
irfft - Inverse of rfft
dct - Discrete cosine transform
idct - Inverse discrete cosine transform
dst - Discrete sine transform
idst - Inverse discrete sine transform
Differential and pseudo-differential operators
==============================================
.. autosummary::
:toctree: generated/
diff - Differentiation and integration of periodic sequences
tilbert - Tilbert transform: cs_diff(x,h,h)
itilbert - Inverse Tilbert transform: sc_diff(x,h,h)
hilbert - Hilbert transform: cs_diff(x,inf,inf)
ihilbert - Inverse Hilbert transform: sc_diff(x,inf,inf)
cs_diff - cosh/sinh pseudo-derivative of periodic sequences
sc_diff - sinh/cosh pseudo-derivative of periodic sequences
ss_diff - sinh/sinh pseudo-derivative of periodic sequences
cc_diff - cosh/cosh pseudo-derivative of periodic sequences
shift - Shift periodic sequences
Helper functions
================
.. autosummary::
:toctree: generated/
fftshift - Shift the zero-frequency component to the center of the spectrum
ifftshift - The inverse of `fftshift`
fftfreq - Return the Discrete Fourier Transform sample frequencies
rfftfreq - DFT sample frequencies (for usage with rfft, irfft)
Note that ``fftshift``, ``ifftshift`` and ``fftfreq`` are numpy functions
exposed by ``fftpack``; importing them from ``numpy`` should be preferred.
Convolutions (:mod:`scipy.fftpack.convolve`)
============================================
.. module:: scipy.fftpack.convolve
.. autosummary::
:toctree: generated/
convolve
convolve_z
init_convolution_kernel
destroy_convolve_cache
"""
# List of possibly useful functions in scipy.fftpack._fftpack:
# drfft
# zfft
# zrfft
# zfftnd
# destroy_drfft_cache
# destroy_zfft_cache
# destroy_zfftnd_cache
from __future__ import division, print_function, absolute_import
__all__ = ['fft','ifft','fftn','ifftn','rfft','irfft',
'fft2','ifft2',
'diff',
'tilbert','itilbert','hilbert','ihilbert',
'sc_diff','cs_diff','cc_diff','ss_diff',
'shift',
'rfftfreq',
'fftfreq', 'fftshift', 'ifftshift'
]
from .fftpack_version import fftpack_version as __version__
from .basic import *
from .pseudo_diffs import *
from .helper import *
from numpy.dual import register_func
for k in ['fft', 'ifft', 'fftn', 'ifftn', 'fft2', 'ifft2']:
register_func(k, eval(k))
del k, register_func
from .realtransforms import *
__all__.extend(['dct', 'idct', 'dst', 'idst'])
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
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