# 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 multi-dimensional discrete Fourier transform of x. ifftn(x[, shape, axes, overwrite_x]) Return inverse multi-dimensional discrete Fourier transform of 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.

## Differential and pseudo-differential operators¶

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

## 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: