Derive the z-transforms for the time functions listed
Chapter 13, Problem 1(choose chapter or problem)
Derive the z-transforms for the time functions listed below. Do not use any z-transform tables. Use the plan \(f(t) \rightarrow f^*(t) \rightarrow F^*(s) \rightarrow F(z)\), followed by converting F(z) into closed form making use of the fact that \(1 /\left(1-z^{-1}\right)=1+z^{-1}+z^{-2}+z^{-3}+\cdots\). Assume ideal sampling. [Section: 13.3]
(a) \(e^{-a t} u(t)\)
(b) u(t)
(c) \(t^2 e^{-a t} u(t)\)
(d) \(\cos \omega t u(t)\)
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