**Example 7.4** Convolve and

**Solution**

Let

which gives

*z*(0) = *x*(0)*y*(0)

*z*(1) = *x*(0)*y*(1) + *x*(1)*y*(0)

*z*(2) = *x*(0)*y*(2) + *x*(1)*y*(1) + *x*(2)*y*(0)

*z*(3) = *x*(0)*y*(3) + *x*(1)*y*(2) + *x*(2)*y*(1) + *x* (3)*y*(0)

Here

*x*(0) = 1, *x*(1) = 2, *x* (2) = 3 and *x* (3) = 4 and

*y*(0) = 1, *y* (1) = –2, *y* (2) = 0. *y* (3) = 0

*z*(0) = *x* (0)*y*(0) = 1 × 1 = 1

*z*(1) = *x* (0)*y*(1) + *x* (1)*y*(0) = 1 × (–2) + 2 × (1) = 0

*z*(2) = *x* (0)*y*(2) + *x* (1)*y*(1) + *x* (2)*y*(0) = 1 × 0 + 2 ...

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