Example 2.8 Find f(t) g(t) for the functions f(t) and g(t) shown in Figs. 2.10a and 2.10b. Here, f(t) has a simpler mathematical description than that of g(t), so it is preferable to invert f(t). Hence, we shall determine g(t) f(t) rather than f(t) *g(t). Thus c(t) = g(t)f(t) = g(T)f(t-r) dr 2.4 System Response to External Input: The Zero-State Response f(t) 8 (1) 1 f(-1) -1 0 -I 1 I 8(T) (a) (c) 31- f(1-x) 8(x) -Isisl -1+1 0 1+1 3- (b) (d) 川 f(1-x) 1+1- 1+1 3 1st≤2 8 (1) (e) f(1-x) 8(x) 2sts4 135 f(1-T) 8 (T) 1-1 0 1+1- 8(x) 3 1+1 x- f(1-T) (f) 124 пи ип 1+1- c(r) (h) -1+1 (g) +(1+1)² -1 0 1 2 3 (i) -(2-21-8) Fig. 2.10 Convolution of f(t) and g(t) in Example 2.8.