ECE535_10S_hw1

ECE535_10S_hw1 - ECE 535 DISCRETE TIME SYSTEMS SPRING 2010...

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Unformatted text preview: ECE 535 DISCRETE TIME SYSTEMS SPRING 2010 HOMEWORK ASSIGNMENT #1 Due: 27 January 2010 1. Use the z-transform to solve the difference equation y ( k )- . 625 y ( k- 1) + 0 . 0625 y ( k- 2) = 53 u ( k- 1)- 25 u ( k- 2) u ( k ) = ‰ k/ 8 , k ≥ , k < y ( k ) = 0 , k < . Also use Matlab to solve this equation. Do this using the lsim command (where the “ SYS ” argument of the command represents the transfer function of the system), and also using the impulse command of Matlab (where for the “ SYS ” argument of the command you use the z-tranform of the output Y ( z ) (why?)). Plot (using Matlab ) the response you determined via z-transform analysis, together with the two responses computing using Matlab . Plot all three on the same set of axes. 2. Consider the discrete-time system described by x ( k + 1) = • 2- (1 / 18) 1 ‚ x ( k ) + • 1 ‚ u ( k ) y ( k ) = £ 1- 1 / x ( k ) (a) Compute the transfer function....
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ECE535_10S_hw1 - ECE 535 DISCRETE TIME SYSTEMS SPRING 2010...

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