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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