# 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, overwrite_x]) 2-D discrete Fourier transform. ifft2(x[, shape, axes, overwrite_x]) 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 the zero-frequency component to the center of the spectrum. ifftshift(x[, axes]) The inverse of fftshift. dftfreq 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:

## 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: