scipy.signal.

convolve#

scipy.signal.convolve(in1, in2, mode='full', method='auto')[source]#

Convolve two N-dimensional arrays.

Convolve in1 and in2, with the output size determined by the mode argument.

Parameters:

in1array_like

First input.

in2array_like

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

modestr {‘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.

methodstr {‘auto’, ‘direct’, ‘fft’}, optional

A string indicating which method to use to calculate the convolution.

direct: The convolution is determined directly from sums, the definition of convolution.
fft: The Fourier Transform is used to perform the convolution by calling fftconvolve.
auto: Automatically chooses direct or Fourier method based on an estimate of which is faster (default). See Notes for more detail.

Added in version 0.19.0.

Returns:

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

Warns:

RuntimeWarning: Use of the FFT convolution on input containing NAN or INF will lead to the entire output being NAN or INF. Use method=’direct’ when your input contains NAN or INF values.

See also

numpy.polymul: performs polynomial multiplication (same operation, but also accepts poly1d objects)
choose_conv_method: chooses the fastest appropriate convolution method
fftconvolve: Always uses the FFT method.
oaconvolve: Uses the overlap-add method to do convolution, which is generally faster when the input arrays are large and significantly different in size.

Notes

By default, convolve and correlate use method='auto', which calls choose_conv_method to choose the fastest method using pre-computed values (choose_conv_method can also measure real-world timing with a keyword argument). Because fftconvolve relies on floating point numbers, there are certain constraints that may force method='direct' (more detail in choose_conv_method docstring).

Array API Standard Support

convolve 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

CuPy does not support inputs with ndim>1 when method="auto" but does support higher dimensional arrays for method="direct" and method="fft".

See Support for the array API standard for more information.

Examples

Smooth a square pulse using a Hann window:

>>> import numpy as np
>>> from scipy import signal
>>> sig = np.repeat([0., 1., 0.], 100)
>>> win = signal.windows.hann(50)
>>> filtered = signal.convolve(sig, win, mode='same') / sum(win)

>>> import matplotlib.pyplot as plt
>>> fig, (ax_orig, ax_win, ax_filt) = plt.subplots(3, 1, sharex=True)
>>> ax_orig.plot(sig)
>>> ax_orig.set_title('Original pulse')
>>> ax_orig.margins(0, 0.1)
>>> ax_win.plot(win)
>>> ax_win.set_title('Filter impulse response')
>>> ax_win.margins(0, 0.1)
>>> ax_filt.plot(filtered)
>>> ax_filt.set_title('Filtered signal')
>>> ax_filt.margins(0, 0.1)
>>> fig.tight_layout()
>>> fig.show()

../../_images/scipy-signal-convolve-1.png