Homework 8 EE235, Spring 2012 Solutions 1. Find the (unilateral ...

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(d) We form another causal LTI system, whose system transfer function

is H1(s) = (s + 2 + j)H(s). Let h1(t) be the impulse response of this

new system. Is h1(t) a real signal? Justify your answer.

Since

H1(s) = (s + 2 + j)H(s) =

A

(s + 3)(s + 2 − j)(s − 1) ,

which has three poles, h1(t) cannot be real, because for real signals,

if they have complex poles or zeros, they must be in conjugate pairs.

Here for H1(s), it has a complex pole at s = −2 + j, but it does not

have a pole at s = −2 − j, so h1(t) cannot be real.

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(d) We form another causal LTI system, whose system transfer function is H1(s) = (s + 2 + j)H(s). Let h1(t) be the impulse response of this new system. Is h1(t) a real signal? Justify your answer. Since H1(s) = (s + 2 + j)H(s) = A (s + 3)(s + 2 − j)(s − 1) , which has three poles, h1(t) cannot be real, because for real signals, if they have complex poles or zeros, they must be in conjugate pairs. Here for H1(s), it has a complex pole at s = −2 + j, but it does not have a pole at s = −2 − j, so h1(t) cannot be real. 6

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Page 3 and 4: The initial value theorem states li
Page 5: (b) Does a stable and causal invers

Homework 8 EE235, Spring 2012 Solutions 1. Find the (unilateral ...

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