The convolution of a pair of sequences a(n) and b(n) is written

The convolution of a pair of sequences a(n) and b(n) is written as

c(n) = a ∗ b(n) =

m

a(m)b(n − m).

Make a pair of polynomials for a(n) and b(n) such that

A(X) =

n

a(n)Xn (2.95)

B(X) =

n

b(n)Xn.

Suppose the corresponding polynomial for c(n) is defined as

Fig. 2.7 Schematic for the

convolution of Exercise 6

C(X) = A(X)B(X) =

n

cˆ(n)Xn.

Show

cˆ(n) = a ∗ b(n) = c(n).


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