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# Fourier transforms (`scipy.fftpack`)

## Fast Fourier transforms

`fft`(x[, n, axis, overwrite_x]) | Return discrete Fourier transform of arbitrary type sequence x.
`ifft`(x[, n, axis, overwrite_x]) | Return discrete inverse Fourier transform of real or complex sequence.
`fftn`(x[, shape, axes, overwrite_x]) | fftn(x, shape=None, axes=None, overwrite_x=0) -> y
`ifftn`(x[, shape, axes, overwrite_x]) | Return inverse multi-dimensional discrete Fourier transform of
`fft2`(x[, shape, axes, overwrite_x]) | 2-D discrete Fourier transform.
`ifft2`(x[, shape, axes, overwrite_x]) | 2-D discrete inverse Fourier transform of real or complex sequence.
`rfft`(x[, n, axis, overwrite_x]) | Discrete Fourier transform of a real sequence.
`irfft`(x[, n, axis, overwrite_x]) | irfft(x, n=None, axis=-1, overwrite_x=0) -> y

## Differential and pseudo-differential operators

`diff`(x[, order, period, _cache]) | diff(x, order=1, period=2*pi) -> y
`tilbert`(x, h[, period, _cache]) | tilbert(x, h, period=2*pi) -> y
`itilbert`(x, h[, period, _cache]) | itilbert(x, h, period=2*pi) -> y
`hilbert`(x[, _cache]) | hilbert(x) -> y
`ihilbert`(x) | ihilbert(x) -> y
`cs_diff`(x, a, b[, period, _cache]) | cs_diff(x, a, b, period=2*pi) -> y
`sc_diff`(x, a, b[, period, _cache]) | Return (a,b)-sinh/cosh pseudo-derivative of a periodic sequence x.
`ss_diff`(x, a, b[, period, _cache]) | ss_diff(x, a, b, period=2*pi) -> y
`cc_diff`(x, a, b[, period, _cache]) | cc_diff(x, a, b, period=2*pi) -> y
`shift`(x, a[, period, _cache]) | shift(x, a, period=2*pi) -> y

## Helper functions

`fftshift`(x[, axes]) | Shift the zero-frequency component to the center of the spectrum.
`ifftshift`(x[, axes]) | The inverse of fftshift.
`fftfreq`(n[, d]) | Return the Discrete Fourier Transform sample frequencies.
`rfftfreq`(n[, d]) | rfftfreq(n, d=1.0) -> f

## Convolutions (`scipy.fftpack.convolve`)

`convolve` | convolve - Function signature:
`convolve_z` | convolve_z - Function signature:
`init_convolution_kernel` | init_convolution_kernel - Function signature:
`destroy_convolve_cache` | destroy_convolve_cache - Function signature:

## Other (`scipy.fftpack._fftpack`)

`drfft` | drfft - Function signature:
`zfft` | zfft - Function signature:
`zrfft` | zrfft - Function signature:
`zfftnd` | zfftnd - Function signature:
`destroy_drfft_cache` | destroy_drfft_cache - Function signature:
`destroy_zfft_cache` | destroy_zfft_cache - Function signature:
`destroy_zfftnd_cache` | destroy_zfftnd_cache - Function signature:

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