ECE130A-F10-HW08 - ECE 130A Signal Analysis and Processing...

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ECE 130A: Signal Analysis and Processing Prof. Michael Liebling Fall 2010 TAs: Jingning Han, Hari Sivakumar Distribution: Monday, 22 November 2010 Electrical & Computer Engineering Dept. Homework Due: Wednesday, 1 December 2010 at 7:00 p.m. University of California, Santa Barbara Homework 8 Problem 1: System Function Algebra for Interconnected LTI Systems (40 Points) The input x ( t ) and output y ( t ) of a causal LTI system are re- lated through the block diagram representation shown on the right. (a) Determine a differential equation relating y ( t ) and x ( t ). (b) Is this system stable? + + + + -1 -2 1 s 1 s -1 -6 x ( t ) y ( t ) Problem 2: Systems with Feedback (30 Points) A causal LTI system S with input x ( t ) and output y ( t ), as depicted below, is characterized by the following differential equation: d d t y ( t ) + 2 y ( t ) = 1 10 x ( t ) x ( t ) y ( t ) S (a) Find the output if the input is x ( t ) = cos2 t . (b) Suppose that you introduce feedback into the system as shown below. x ( t ) y ( t ) S + -2 Find the output if the input is x ( t ) = cos2 t .
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