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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 

dctn - n-dimensional Discrete cosine transform 

idctn - n-dimensional Inverse discrete cosine transform 

dst - Discrete sine transform 

idst - Inverse discrete sine transform 

dstn - n-dimensional Discrete sine transform 

idstn - n-dimensional 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) 

next_fast_len - Find the optimal length to zero-pad an FFT for speed 

 

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', 

'fftfreq', 'rfftfreq', 

'fftshift', 'ifftshift', 

'next_fast_len', 

] 

 

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', 'dctn', 'idctn', 'dstn', 

'idstn']) 

 

from scipy._lib._testutils import PytestTester 

test = PytestTester(__name__) 

del PytestTester