Consider the following impulse responses h 1 (t) (2 3)e 2t (1 3)e t u(t), h 2 (t) (2 3)e 2t u(t) (1 3)e t u( t), h 3 (t) (2 3)e 2t u( t) (1 3)e t u( t) (a) From the expression for h 1 (t)determine if the system is causal and BIBO stable Find its Laplace transform H 1 (s)and its region of convergenc...

ac h 1 t is unbounded and corresponds to an unstable causal system h 2 t ...

Consider the following impulse responses h 1 (t) = [(2/3)e 2t + (1/3)e t ] u(t), h

Question:

Consider the following impulse responses

h₁(t) = [(2/3)e^−2t + (1/3)e^t] u(t),

h₂(t) = (2/3)e^−2t u(t) − (1/3)e^t u( − t),

h₃(t) = −(2/3)e^−2t u( − t) − (1/3)e^t u( − t)

(a) From the expression for h₁(t)determine if the system is causal and BIBO stable. Find its Laplace transform H₁(s)and its region of convergence.

(b) From the expression for h₂(t)determine if the system is non-causal and BIBO stable. Find its Laplace transform H₂(s)and its region of convergence.

(c) From the expression for h₃(t)determine if the system is anti-causal and BIBO stable. Find its Laplace transform H₃(s)and its region of convergence.

(d) From the above, determine the general condition for a system to be BIBO stable.

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