`scipy.fft._basic:rfft`

source: build-install/usr/lib/python3.14/site-packages/scipy/fft/_basic.py:278

Signature

def rfft(x, n = None, axis = -1, norm = None, overwrite_x = False, workers = None, *, plan = None)

Summary

Compute the 1-D discrete Fourier Transform for real input.

Extended Summary

This function computes the 1-D n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).

Parameters

x : array_like: Input array
n : int, optional: Number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.
axis : int, optional: Axis over which to compute the FFT. If not given, the last axis is used.
norm : {"backward", "ortho", "forward"}, optional: Normalization mode (see fft). Default is "backward".
overwrite_x : bool, optional: If True, the contents of x can be destroyed; the default is False. See fft for more details.
workers : int, optional: Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count(). See fft for more details.
plan : object, optional: This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.
versionadded 1.5.0

Returns

out : complex ndarray: The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. If n is even, the length of the transformed axis is (n/2)+1. If n is odd, the length is (n+1)/2.

Raises

: IndexError: If axis is larger than the last axis of a.

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 X = rfft(x) and fs is the sampling frequency, X[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 scipy.fft

✓

scipy.fft.fft([0, 1, 0, 0])
scipy.fft.rfft([0, 1, 0, 0])

✗

array([ 1.+0.j,  0.-1.j, -1.+0.j])

Notice how the final element of the `fft` output is the complex conjugate of the second element, for real input. For `rfft`, this symmetry is exploited to compute only the non-negative frequency terms.

Aliases

scipy.fft.rfft