scipy.fftpack.rfft¶
-
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]
. Ifn < x.shape[axis]
, x is truncated, ifn > 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)*j*k*2*pi/n) j = 0..n-1
See also
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 related function
numpy.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.])