rfft — SciPy v1.15.3 Manual (original) (raw)

scipy.fftpack.

scipy.fftpack.rfft(x, n=None, axis=-1, overwrite_x=False)[source]#

Discrete Fourier transform of a real sequence.

Parameters:

xarray_like, real-valued

The data to transform.

nint, optional

Defines the length of the Fourier transform. If n is not specified (the default) then n = x.shape[axis]. If n < x.shape[axis],x is truncated, if n > x.shape[axis], x is zero-padded.

axisint, optional

The axis along which the transform is applied. The default is the last axis.

overwrite_xbool, optional

If set to true, the contents of x can be overwritten. Default is False.

Returns:

zreal ndarray

The returned real array contains:

[y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2))] if n is even [y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2)),Im(y(n/2))] if n is odd

where:

y(j) = sum[k=0..n-1] x[k] * exp(-sqrt(-1)jk2pi/n) j = 0..n-1

Notes

Within numerical accuracy, y == rfft(irfft(y)).

Both single and double precision routines are implemented. Half precision inputs will be converted to single precision. Non-floating-point inputs will be converted to double precision. Long-double precision inputs are not supported.

To get an output with a complex datatype, consider using the newer function scipy.fft.rfft.

Examples

from scipy.fftpack import fft, rfft a = [9, -9, 1, 3] fft(a) array([ 4. +0.j, 8.+12.j, 16. +0.j, 8.-12.j]) rfft(a) array([ 4., 8., 12., 16.])