# 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()