Consider a causal continuous time system with impulse response h c (t) and system function (a) Use impulse invariance to determine H 1 (z) for a discrete time system such that h 1 n h c (n T) (b) Use step invariance to determine H 2 (z) for a discrete time system such that s 2 n s c (n T), where (c) Determine the step response s 1 n of system 1 and the impulse response h 2 n of system 2 Is it true that h 2 n h 1 n h c (n T) Is it true that s 1 n s 2 n s c (n T) s a H (s) (s a)2 b2 Part B s2 n ha k h (t)dr and Se(t) k 00

Question: Consider a causal continuous-time system with impulse response h c (t) and system function? (a) Use impulse invariance to determine H 1 (z) for a

Consider a causal continuous-time system with impulse response h_c(t) and system function?

(a) Use impulse invariance to determine H₁(z) for a discrete-time system such that h₁[n] = h_c(n T).

(b) Use step invariance to determine H₂(z) for a discrete-time system such that s₂[n] = s_c(n T), where

s + a H.(s)= (s +a)2 + b2 Part B s2[n] =

(c) Determine the step response s₁[n] of system 1 and the impulse response h₂[n] of system 2. Is it true that h₂[n] = h₁[n] = h_c(n T)? Is it true that s₁[n] = s₂[n] = s_c(n T)?

s + a H.(s)= (s +a)2 + b2 Part B s2[n] = ha[k] | h:(t)dr. and Se(t) = k=-00

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