Signals and Systems

ADDITIONAL SOLVED EXAMPLES

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 ...