Assume that Hc(s) has an rth-order pole at s = s0, so that Hc(s) can be expressed as...

Assume that H_c(s) has an r^th-order pole at s = s₀, so that H_c(s) can be expressed as

where G_c(s) has only 1^st-order poles. Assume H_c(s) is causal.

(a) Give a formula for determining the constants A_k from H_c(s).

(b) Obtain an expression for the impulse response hc(t) in terms of s₀ and g_c(t), the inverse Laplace transform of G_c(s).