bundles / numpy 2.4.4 / numpy / fft / rfft
_ArrayFunctionDispatcher
numpy.fft:rfft
source: /numpy/fft/_pocketfft.py :324
Signature
def rfft ( a , n = None , axis = -1 , norm = None , out = None ) Summary
Compute the one-dimensional discrete Fourier Transform for real input.
Extended Summary
This function computes the one-dimensional n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).
Parameters
a: array_likeInput array
n: int, optionalNumber of points along transformation axis in the input to use. If
nis smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. Ifnis not given, the length of the input along the axis specified byaxisis used.axis: int, optionalAxis over which to compute the FFT. If not given, the last axis is used.
norm: {"backward", "ortho", "forward"}, optionalNormalization mode (see numpy.fft). Default is "backward". Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor.
out: complex ndarray, optionalIf provided, the result will be placed in this array. It should be of the appropriate shape and dtype.
Returns
out: complex ndarrayThe truncated or zero-padded input, transformed along the axis indicated by
axis, or the last one ifaxisis not specified. Ifnis even, the length of the transformed axis is(n/2)+1. Ifnis odd, the length is(n+1)/2.
Raises
: IndexErrorIf
axisis not a valid axis ofa.
Notes
When the DFT is computed for purely real input, the output is Hermitian-symmetric, i.e. the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore n//2 + 1.
When A = rfft(a) and fs is the sampling frequency, A[0] contains the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
If n is even, A[-1] contains the term representing both positive and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely real. If n is odd, there is no term at fs/2; A[-1] contains the largest positive frequency (fs/2*(n-1)/n), and is complex in the general case.
If the input a contains an imaginary part, it is silently discarded.
Examples
import numpy as np
✓np.fft.fft([0, 1, 0, 0]) np.fft.rfft([0, 1, 0, 0])✗
See also
Aliases
-
numpy.fft.rfft