Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Discrete convoluti

For complex-valued functions f, g defined on the set Z of integers, the discrete convolution of f and g is given by:

$(f * g)[n] stackrel{mathrm{def}}{=} sum_{m=-infty}^infty f[m], g[n - m]$
$= sum_{m=-infty}^infty f[n-m], g[m].$       (commutativity)

When multiplying two polynomials, the coefficients of the product are given by the convolution of the original coefficient sequences, extended with zeros where necessary to avoid undefined terms; this is known as the Cauchy product of the coefficients of the two polynomials.

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