 $y[0]=x[0]h[0]$
 $y[1] = x[0]h[1] + x[1]h[0]y[1]$
 $y[2] = x[0]h[2] + x[1]h[1] + x[2]h[0]$

1-D convolution is implemented in SciPy using the function convolve

San Jose State University

Convolution explains the connection between input signal ( $x[n]$ ) ,impulse response ( $h[n]$) and the output signal ( $y[n] $).

              $y[n] = x[n]*h[n]$

Convolution of 1-D signal can also be expressed as

             $ y[n] = \sum_{k=-\infty}^{+\infty} x[k] h[n-k]$

Discrete convolution can be expressed as 

           $y [n] = \sum_{k=max(n-M,0)}^{min(n,K)} x[k] h[n-k]$

In the above expression $x[n]$ and $h[n]$ are signals having finite length of  K+1 and M+1 respectively resulting in a finite signal of length K+M+1.



Convolution

https://docs.scipy.org/doc/scipy/tutorial/index.html

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