Legacy discrete Fourier transforms (`scipy.fftpack`)¶

Warning

This submodule is now considered legacy, new code should use scipy.fft.

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 multidimensional discrete Fourier transform.
`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.
`dctn`(x[, type, shape, axes, norm, overwrite_x])	Return multidimensional Discrete Cosine Transform along the specified axes.
`idctn`(x[, type, shape, axes, norm, overwrite_x])	Return multidimensional Discrete Cosine Transform along the specified axes.
`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.
`dstn`(x[, type, shape, axes, norm, overwrite_x])	Return multidimensional Discrete Sine Transform along the specified axes.
`idstn`(x[, type, shape, axes, norm, overwrite_x])	Return multidimensional Discrete Sine Transform along the specified axes.

Differential and pseudo-differential operators¶

`diff`(x[, order, period, _cache])	Return kth 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).
`next_fast_len`(target)	Find the next fast size of input data to `fft`, for zero-padding, etc.

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`()

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