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 [R17]. In
probability theory, the sum of two independent random variables is
distributed according to the convolution of their individual
distributions.
Parameters : | a : (N,) array_like
First one-dimensional input array.
v : (M,) array_like
Second one-dimensional input array.
mode : {‘full’, ‘valid’, ‘same’}, optional
- ‘full’:
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.
- ‘same’:
Mode same returns output of length max(M, N). Boundary
effects are still visible.
- ‘valid’:
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.
|
Returns : | out : ndarray
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.
Notes
The discrete convolution operation is defined as
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It can be shown that a convolution
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in time/space
is equivalent to the multiplication
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in the Fourier
domain, after appropriate padding (padding is necessary to prevent
circular convolution). Since multiplication is more efficient (faster)
than convolution, the function scipy.signal.fftconvolve exploits the
FFT to calculate the convolution of large data-sets.
References
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])