Question

(15 points) Stability: Consider the following list of poles and zeros: • (Three) Poles: (.5 + .5$i$), (.5 - .5$i$), (-.25) • (Two) Zeros: (2), (-1.5) (a) Plot the poles and zeros in the complex plane. (b) If the Laplace transform of the impulse response of a causal LTI system is rational and has the above poles and zeros, is it stable? What is the region of convergence for the Laplace transform of a system that is stable but perhaps not causal and has the same poles and zeros. Is the causal inverse to this system stable? (c) Answer the same questions as above for a discrete-time system, where the stated poles and zeros correspond to a rational Z-transform. Also, considering this system as a filter, approximately which frequency is amplified the most?

          (15 points) Stability: Consider the following list of poles and zeros:
• (Three) Poles: (.5 + .5$i$), (.5 - .5$i$), (-.25)
• (Two) Zeros: (2), (-1.5)
(a) Plot the poles and zeros in the complex plane.
(b) If the Laplace transform of the impulse response of a causal LTI system is rational and
has the above poles and zeros, is it stable? What is the region of convergence for the
Laplace transform of a system that is stable but perhaps not causal and has the same
poles and zeros. Is the causal inverse to this system stable?
(c) Answer the same questions as above for a discrete-time system, where the stated poles
and zeros correspond to a rational Z-transform. Also, considering this system as a filter,
approximately which frequency is amplified the most?

(15 points) Stability: Consider the following list of poles and zeros:
• (Three) Poles: (.5 + .5i), (.5 - .5i), (-.25)
• (Two) Zeros: (2), (-1.5)
(a) Plot the poles and zeros in the complex plane.
(b) If the Laplace transform of the impulse response of a causal LTI system is rational and
has the above poles and zeros, is it stable? What is the region of convergence for the
Laplace transform of a system that is stable but perhaps not causal and has the same
poles and zeros. Is the causal inverse to this system stable?
(c) Answer the same questions as above for a discrete-time system, where the stated poles
and zeros correspond to a rational Z-transform. Also, considering this system as a filter,
approximately which frequency is amplified the most?

Added by Michelle W.

Question

Please give Ace some feedback