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1"""
2=========================================================
3Legacy discrete Fourier transforms (:mod:`scipy.fftpack`)
4=========================================================
6.. warning::
8 This submodule is now considered legacy, new code should use
9 :mod:`scipy.fft`.
11Fast Fourier Transforms (FFTs)
12==============================
14.. autosummary::
15 :toctree: generated/
17 fft - Fast (discrete) Fourier Transform (FFT)
18 ifft - Inverse FFT
19 fft2 - 2-D FFT
20 ifft2 - 2-D inverse FFT
21 fftn - N-D FFT
22 ifftn - N-D inverse FFT
23 rfft - FFT of strictly real-valued sequence
24 irfft - Inverse of rfft
25 dct - Discrete cosine transform
26 idct - Inverse discrete cosine transform
27 dctn - N-D Discrete cosine transform
28 idctn - N-D Inverse discrete cosine transform
29 dst - Discrete sine transform
30 idst - Inverse discrete sine transform
31 dstn - N-D Discrete sine transform
32 idstn - N-D Inverse discrete sine transform
34Differential and pseudo-differential operators
35==============================================
37.. autosummary::
38 :toctree: generated/
40 diff - Differentiation and integration of periodic sequences
41 tilbert - Tilbert transform: cs_diff(x,h,h)
42 itilbert - Inverse Tilbert transform: sc_diff(x,h,h)
43 hilbert - Hilbert transform: cs_diff(x,inf,inf)
44 ihilbert - Inverse Hilbert transform: sc_diff(x,inf,inf)
45 cs_diff - cosh/sinh pseudo-derivative of periodic sequences
46 sc_diff - sinh/cosh pseudo-derivative of periodic sequences
47 ss_diff - sinh/sinh pseudo-derivative of periodic sequences
48 cc_diff - cosh/cosh pseudo-derivative of periodic sequences
49 shift - Shift periodic sequences
51Helper functions
52================
54.. autosummary::
55 :toctree: generated/
57 fftshift - Shift the zero-frequency component to the center of the spectrum
58 ifftshift - The inverse of `fftshift`
59 fftfreq - Return the Discrete Fourier Transform sample frequencies
60 rfftfreq - DFT sample frequencies (for usage with rfft, irfft)
61 next_fast_len - Find the optimal length to zero-pad an FFT for speed
63Note that ``fftshift``, ``ifftshift`` and ``fftfreq`` are numpy functions
64exposed by ``fftpack``; importing them from ``numpy`` should be preferred.
66Convolutions (:mod:`scipy.fftpack.convolve`)
67============================================
69.. module:: scipy.fftpack.convolve
71.. autosummary::
72 :toctree: generated/
74 convolve
75 convolve_z
76 init_convolution_kernel
77 destroy_convolve_cache
79"""
82__all__ = ['fft','ifft','fftn','ifftn','rfft','irfft',
83 'fft2','ifft2',
84 'diff',
85 'tilbert','itilbert','hilbert','ihilbert',
86 'sc_diff','cs_diff','cc_diff','ss_diff',
87 'shift',
88 'fftfreq', 'rfftfreq',
89 'fftshift', 'ifftshift',
90 'next_fast_len',
91 'dct', 'idct', 'dst', 'idst', 'dctn', 'idctn', 'dstn', 'idstn'
92 ]
94from .basic import *
95from .pseudo_diffs import *
96from .helper import *
97from .realtransforms import *
99from scipy._lib._testutils import PytestTester
100test = PytestTester(__name__)
101del PytestTester