`scipy.fft._basic:rfft`

source: /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.

Array API Standard Support

rfft has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import scipy.fft

✓

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

✗

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