The one-sided z-transform is defined as (a) Show that the one-sided transform of . (b)
Chapter 8, Problem 8.3(choose chapter or problem)
The one-sided z-transform is defined as (a) Show that the one-sided transform of . (b) Use the one-sided transform to solve for the transforms of the Fibonacci numbers generated by the difference equation u(k) + 2) = u(k) + 1) + u(k) . Let u( 0) = u(1) = 1. [Hint: You will need to find a general expression for the transform of f(k + 2) in terms of the transform of f(k).] (c) Compute the pole locations of the transform of the Fibonacci numbers. (d) Compute the inverse transform of the Fibonacci numbers. (e) Show that, if u(k) represents the k th Fibonacci number, then the ratio u(k) + 1)/u(k) will approach . This is the golden ratio valued so highly by the Greeks.
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