scipy.fftpack.rfft¶
- scipy.fftpack.rfft(x, n=None, axis=-1, overwrite_x=False)[source]¶
Discrete Fourier transform of a real sequence.
Parameters: x : array_like, real-valued
The data to transform.
n : int, 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.
axis : int, optional
The axis along which the transform is applied. The default is the last axis.
overwrite_x : bool, optional
If set to true, the contents of x can be overwritten. Default is False.
Returns: z : real 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
Note that y(-j) == y(n-j).conjugate().
Notes
Within numerical accuracy, y == rfft(irfft(y)).
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.])