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Consider the following system functions for stable LTI systems. Without utilizing the

Chapter 10, Problem 10.16

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QUESTION:

Consider the following system functions for stable LTI systems. Without utilizing the inverse z-transform, determine in each case whether or not the corresponding system is causal. 1 4 -1 + I -2 (a) - 3z 2z z- 1(1- 4z- 1)(1- ~z- ) (b) (c) z-! 2 2 I _ 3 z + 2z 16 z + 1 z +:!- !z-2 - ~z- 3

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QUESTION:

Consider the following system functions for stable LTI systems. Without utilizing the inverse z-transform, determine in each case whether or not the corresponding system is causal. 1 4 -1 + I -2 (a) - 3z 2z z- 1(1- 4z- 1)(1- ~z- ) (b) (c) z-! 2 2 I _ 3 z + 2z 16 z + 1 z +:!- !z-2 - ~z- 3

ANSWER:

Step 1 of 4

(a)

Calculating the poles of a given system function. Equating the denominator to zero,

For the first term,

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