numpy.
convolve
Returns the discrete, linear convolution of two one-dimensional sequences.
The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [1]. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions.
If v is longer than a, the arrays are swapped before computation.
First one-dimensional input array.
Second one-dimensional input array.
By default, mode is ‘full’. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen.
Mode ‘same’ returns output of length max(M, N). Boundary effects are still visible.
max(M, N)
Mode ‘valid’ returns output of length max(M, N) - min(M, N) + 1. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect.
max(M, N) - min(M, N) + 1
Discrete, linear convolution of a and v.
See also
scipy.signal.fftconvolve
Convolve two arrays using the Fast Fourier Transform.
scipy.linalg.toeplitz
Used to construct the convolution operator.
polymul
Polynomial multiplication. Same output as convolve, but also accepts poly1d objects as input.
Notes
The discrete convolution operation is defined as
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It can be shown that a convolution
System Message: WARNING/2 (x(t) * y(t))
System Message: WARNING/2 (X(f) Y(f))
References
Wikipedia, “Convolution”, https://en.wikipedia.org/wiki/Convolution
Examples
Note how the convolution operator flips the second array before “sliding” the two across one another:
>>> np.convolve([1, 2, 3], [0, 1, 0.5]) array([0. , 1. , 2.5, 4. , 1.5])
Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account:
>>> np.convolve([1,2,3],[0,1,0.5], 'same') array([1. , 2.5, 4. ])
The two arrays are of the same length, so there is only one position where they completely overlap:
>>> np.convolve([1,2,3],[0,1,0.5], 'valid') array([2.5])
