Returns the discrete, linear convolution of two onedimensional sequences.
The convolution operator is often seen in signal processing, where it models the effect of a linear timeinvariant system on a signal [R27]. 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
v : (M,) array_like
mode : {‘full’, ‘valid’, ‘same’}, optional


Returns:  out : ndarray

See also
Notes
The discrete convolution operation is defined as
It can be shown that a convolution in time/space is equivalent to the multiplication 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 datasets.
References
[R27]  (1, 2) Wikipedia, “Convolution”, http://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])