Discrete Fourier transforms (scipy.fftpack)

Fast Fourier Transforms (FFTs)

fft(x[, n, axis, overwrite_x])	Return discrete Fourier transform of real or complex sequence.
ifft(x[, n, axis, overwrite_x])	Return discrete inverse Fourier transform of real or complex sequence.
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.
fftn(x[, shape, axes, overwrite_x])	Return multidimensional discrete Fourier transform.
ifftn(x[, shape, axes, overwrite_x])	Return inverse multi-dimensional discrete Fourier transform of arbitrary type sequence x.
rfft(x[, n, axis, overwrite_x])	Discrete Fourier transform of a real sequence.
irfft(x[, n, axis, overwrite_x])	Return inverse discrete Fourier transform of real sequence x.
dct(x[, type, n, axis, norm, overwrite_x])	Return the Discrete Cosine Transform of arbitrary type sequence x.
idct(x[, type, n, axis, norm, overwrite_x])	Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.
dst(x[, type, n, axis, norm, overwrite_x])	Return the Discrete Sine Transform of arbitrary type sequence x.
idst(x[, type, n, axis, norm, overwrite_x])	Return the Inverse Discrete Sine Transform of an arbitrary type sequence.

Differential and pseudo-differential operators

diff(x[, order, period, _cache])	Return k-th derivative (or integral) of a periodic sequence x.
tilbert(x, h[, period, _cache])	Return h-Tilbert transform of a periodic sequence x.
itilbert(x, h[, period, _cache])	Return inverse h-Tilbert transform of a periodic sequence x.
hilbert(x[, _cache])	Return Hilbert transform of a periodic sequence x.
ihilbert(x)	Return inverse Hilbert transform of a periodic sequence x.
cs_diff(x, a, b[, period, _cache])	Return (a,b)-cosh/sinh pseudo-derivative of a periodic sequence.
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])	Return (a,b)-sinh/sinh pseudo-derivative of a periodic sequence x.
cc_diff(x, a, b[, period, _cache])	Return (a,b)-cosh/cosh pseudo-derivative of a periodic sequence.
shift(x, a[, period, _cache])	Shift periodic sequence x by a: y(u) = x(u+a).

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])	DFT sample frequencies (for usage with rfft, irfft).

Note that fftshift, ifftshift and fftfreq are numpy functions exposed by fftpack; importing them from numpy should be preferred.

Convolutions (scipy.fftpack.convolve)

convolve(x,omega,[swap_real_imag,overwrite_x])	Wrapper for convolve.
convolve_z(x,omega_real,omega_imag,[overwrite_x])	Wrapper for convolve_z.
init_convolution_kernel(...)	Wrapper for init_convolution_kernel.
destroy_convolve_cache()	Wrapper for destroy_convolve_cache.