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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]) | ifft(x, n=None, axis=-1, overwrite_x=0) -> y
`fftn` (x[, shape, axes, overwrite_x]) | fftn(x, shape=None, axes=None, overwrite_x=0) -> y
`ifftn` (x[, shape, axes, overwrite_x]) | ifftn(x, s=None, axes=None, overwrite_x=0) -> y
`fft2` (x[, shape, axes, -1), ...]) | fft2(x, shape=None, axes=(-2,-1), overwrite_x=0) -> y
`ifft2` (x[, shape, axes, -1), ...]) | ifft2(x, shape=None, axes=(-2,-1), overwrite_x=0) -> y
`rfft` (x[, n, axis, overwrite_x]) | rfft(x, n=None, axis=-1, overwrite_x=0) -> y
`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]) | sc_diff(x, a, b, period=2*pi) -> y
`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 zero-frequency component to center of spectrum.
`ifftshift` (x[, axes]) | Inverse of fftshift.
`dftfreq` |
`rfftfreq` (n[, d]) | rfftfreq(n, d=1.0) -> f

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

`convolve` () | convolve - Function signature: y = convolve(x,omega,[swap_real_imag,overwrite_x]) Required arguments: x : input rank-1 array(‘d’) with bounds (n) omega : input rank-1 array(‘d’) with bounds (n) Optional arguments: overwrite_x := 0 input int swap_real_imag := 0 input int Return objects: y : rank-1 array(‘d’) with bounds (n) and x storage
`convolve_z` () | convolve_z - Function signature: y = convolve_z(x,omega_real,omega_imag,[overwrite_x]) Required arguments: x : input rank-1 array(‘d’) with bounds (n) omega_real : input rank-1 array(‘d’) with bounds (n) omega_imag : input rank-1 array(‘d’) with bounds (n) Optional arguments: overwrite_x := 0 input int Return objects: y : rank-1 array(‘d’) with bounds (n) and x storage
`init_convolution_kernel` () | init_convolution_kernel - Function signature: omega = init_convolution_kernel(n,kernel_func,[d,zero_nyquist,kernel_func_extra_args]) Required arguments: n : input int kernel_func : call-back function Optional arguments: d := 0 input int kernel_func_extra_args := () input tuple zero_nyquist := d%2 input int Return objects: omega : rank-1 array(‘d’) with bounds (n) Call-back functions: def kernel_func(k): return kernel_func Required arguments: k : input int Return objects: kernel_func : float
`destroy_convolve_cache` () | destroy_convolve_cache - Function signature: destroy_convolve_cache()

## `scipy.fftpack._fftpack`

`drfft` () | drfft - Function signature: y = drfft(x,[n,direction,normalize,overwrite_x]) Required arguments: x : input rank-1 array(‘d’) with bounds (*) Optional arguments: overwrite_x := 0 input int n := size(x) input int direction := 1 input int normalize := (direction<0) input int Return objects: y : rank-1 array(‘d’) with bounds (*) and x storage
`zfft` () | zfft - Function signature: y = zfft(x,[n,direction,normalize,overwrite_x]) Required arguments: x : input rank-1 array(‘D’) with bounds (*) Optional arguments: overwrite_x := 0 input int n := size(x) input int direction := 1 input int normalize := (direction<0) input int Return objects: y : rank-1 array(‘D’) with bounds (*) and x storage
`zrfft` () | zrfft - Function signature: y = zrfft(x,[n,direction,normalize,overwrite_x]) Required arguments: x : input rank-1 array(‘D’) with bounds (*) Optional arguments: overwrite_x := 1 input int n := size(x) input int direction := 1 input int normalize := (direction<0) input int Return objects: y : rank-1 array(‘D’) with bounds (*) and x storage
`zfftnd` () | zfftnd - Function signature: y = zfftnd(x,[s,direction,normalize,overwrite_x]) Required arguments: x : input rank-1 array(‘D’) with bounds (*) Optional arguments: overwrite_x := 0 input int s := old_shape(x,j++) input rank-1 array(‘i’) with bounds (r) direction := 1 input int normalize := (direction<0) input int Return objects: y : rank-1 array(‘D’) with bounds (*) and x storage
`destroy_drfft_cache` () | destroy_drfft_cache - Function signature: destroy_drfft_cache()
`destroy_zfft_cache` () | destroy_zfft_cache - Function signature: destroy_zfft_cache()
`destroy_zfftnd_cache` () | destroy_zfftnd_cache - Function signature: destroy_zfftnd_cache()

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