GATE EC 2015 Set 2 — Question 28
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Signals & Systems → Discrete-Time Signals → Inverse Z-Transform
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Question
Two causal discrete-time signals and are related as . If the -transform of is , the value of is ______.
Correct answer
0 to 0
Solution
The relationship represents the accumulation property in discrete time. For causal signals, this is equivalent to , where is the unit step sequence.
1.In the -domain, the accumulation property corresponds to:
2.Rearranging to find :
3.Substitute the given :
4.Express in terms of negative powers of to easily identify the sequence values:
5.Using the power series expansion for (valid for causal signals where ):
6.The sequence is formed by the coefficients of :
- , and so on.
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