# 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.

## 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).

## 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.

## Other (scipy.fftpack._fftpack)¶

 drfft(x,[n,direction,normalize,overwrite_x]) Wrapper for drfft. zfft(x,[n,direction,normalize,overwrite_x]) Wrapper for zfft. zrfft(x,[n,direction,normalize,overwrite_x]) Wrapper for zrfft. zfftnd(x,[s,direction,normalize,overwrite_x]) Wrapper for zfftnd. destroy_drfft_cache() Wrapper for destroy_drfft_cache. destroy_zfft_cache() Wrapper for destroy_zfft_cache. destroy_zfftnd_cache() Wrapper for destroy_zfftnd_cache.

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