There are eight pole-zero graphs of system transfer functions in Figure E.48. Answer the following questions about their frequency responses, impulse responses and step responses. Frequency response:
(a) Which have a phase approaching zero at very high frequencies?
(b) Which have a phase that is discontinuous at zero frequency?
(c) Which have a magnitude approaching zero at high frequencies?
Step response:
(a) Which have a step response that is nonzero in the limit t ? ??
(b) Which have a step response that is discontinuous at t = 0?
Impulse response:
(a) Which have an impulse response that contains an impulse?
(b) Which have an impulse response approaching zero in the limit t ? ??
Frequency response:
(a) A,B,C,D,E (Equal number of finite poles and finite zeros)
(b) D,H (Zero at the origin)
(c) F,G,H (More finite poles than finite zeros)
Step response:
(a) A,B,C,E,F,G (No zero at the origin)
(b) A,B,C,D,E (At least as many finite zeros as finite poles)
Impulse response:
(a) A,B,C,D,E (At least as many finite zeros as finite poles)
(b) A,B,C,D,E,F,G,H (All poles in the open left half-plane)
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