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bundles / scipy 1.17.1 / scipy / signal / _signaltools / fftconvolve

function

scipy.signal._signaltools:fftconvolve

source: /scipy/signal/_signaltools.py :591

Signature

def   fftconvolve ( in1 ,  in2 ,  mode = full ,  axes = None )

Summary

Convolve two N-dimensional arrays using FFT.

Extended Summary

Convolve in1 and in2 using the fast Fourier transform method, with the output size determined by the mode argument.

This is generally much faster than convolve for large arrays (n > ~500), but can be slower when only a few output values are needed, and can only output float arrays (int or object array inputs will be cast to float).

As of v0.19, convolve automatically chooses this method or the direct method based on an estimation of which is faster.

Parameters

in1 : array_like

First input.

in2 : array_like

Second input. Should have the same number of dimensions as in1.

mode : str {'full', 'valid', 'same'}, optional

A string indicating the size of the output:

full

The output is the full discrete linear convolution of the inputs. (Default)

valid

The output consists only of those elements that do not rely on the zero-padding. In 'valid' mode, either in1 or in2 must be at least as large as the other in every dimension.

same

The output is the same size as in1, centered with respect to the 'full' output.

axes : int or array_like of ints or None, optional

Axes over which to compute the convolution. The default is over all axes.

Returns

out : array

An N-dimensional array containing a subset of the discrete linear convolution of in1 with in2.

Notes

Array API Standard Support

fftconvolve 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                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Autocorrelation of white noise is an impulse. 
import numpy as np
from scipy import signal
rng = np.random.default_rng()
sig = rng.standard_normal(1000)
autocorr = signal.fftconvolve(sig, sig[::-1], mode='full')
✓
import matplotlib.pyplot as plt
fig, (ax_orig, ax_mag) = plt.subplots(2, 1)
✓
ax_orig.plot(sig)
ax_orig.set_title('White noise')
ax_mag.plot(np.arange(-len(sig)+1,len(sig)), autocorr)
ax_mag.set_title('Autocorrelation')
✗
fig.tight_layout()
fig.show()
✓
Gaussian blur implemented using FFT convolution. Notice the dark borders around the image, due to the zero-padding beyond its boundaries. The `convolve2d` function allows for other types of image boundaries, but is far slower. 
from scipy import datasets
✓
face = datasets.face(gray=True)
⚠
kernel = np.outer(signal.windows.gaussian(70, 8),
                  signal.windows.gaussian(70, 8))
✓
blurred = signal.fftconvolve(face, kernel, mode='same')
⚠
fig, (ax_orig, ax_kernel, ax_blurred) = plt.subplots(3, 1,
                                                     figsize=(6, 15))
✓
ax_orig.imshow(face, cmap='gray')
⚠
ax_orig.set_title('Original')
✗
ax_orig.set_axis_off()
✓
ax_kernel.imshow(kernel, cmap='gray')
ax_kernel.set_title('Gaussian kernel')
✗
ax_kernel.set_axis_off()
✓
ax_blurred.imshow(blurred, cmap='gray')
⚠
ax_blurred.set_title('Blurred')
✗
ax_blurred.set_axis_off()
fig.show()
✓

See also

convolve

Uses the direct convolution or FFT convolution algorithm depending on which is faster.

oaconvolve

Uses the overlap-add method to do convolution, which is generally faster when the input arrays are large and significantly different in size.

Aliases

  • scipy.signal.fftconvolve

Referenced by

This package

Other packages