Simplified Convolution

Explore a simplified method of convolution that is suitable for discrete-time systems.

Let’s revisit the definition of the convolution expression between the two signals x[n]x[n] and h[n]h[n].

y[n]=mx[m]h[nm]y[n] = \sum_m x[m]h[n-m]

We now know how it can be more easily implemented in discrete-time systems.

Discrete-time implementation

A simplified method implements this procedure right out of the definition itself.

y[n]=+x[1]h[n+1]+x[0]h[n0]+x[1]h[n1]+x[2]h[n2]+y[n] = \cdots + x[-1]h[n+1] + x[0]h[n-0]+x[1]h[n-1]+x[2]h[n-2]+\cdots

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