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Unformatted text preview: University of California, Santa Barbara Department of Electrical & Computer Engineering ECE 147b: Digital Control Winter 2009 Homework 1. Due 5.00pm Friday, 16th January, 2009 in the homework boxes on the 3rd floor of Harold Frank Hall. Problem 1. For each of the following discrete time sequences, calculate the z-transform, plot the poles and zeros and indicate on the plot the region of convergence. a) y ( k ) = braceleftbigg 2 k + ( 1 4 ) k , k ≥ , k < b) y ( k ) = 4 4 | k | c) y ( k ) = - 1 /k- 3 ≤ k ≤ - 1 1 /k 1 ≤ k ≤ 3 otherwise d) y ( k ) = braceleftbigg 1 k =- 5 otherwise Problem 2. Find y ( k ), the inverse bilateral z-Transform of Y ( z ) =- z + 0 . 5 ( z- 1)( z- . 4) , for the following regions of convergence: a) | z | < . 4, b) | z | > 1, c) 0 . 4 < | z | < 1 . In each of the cases a) to c) use the discrete-time domain expressions to give the value of y ( k ), in the limit as k-→ ∞ . Compare your results to those obtained by applying the final value theorem.....
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- Winter '08
- forward difference approximation, Harold Frank Hall, backward difference approximation, Bilinear approximation