ECE130A-HW03-F10 - 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, 11 October 2010 Electrical & Computer Engineering Dept. Homework Due: Tuesday, 19 October 2010, 6:00pm University of California, Santa Barbara Homework 3 Problem 1: Matched filter (20 points) The matched filter for a signal s ( t ) is defined as an LTI system with impulse response h ( t ) = s ( - t ). (a) For s ( t ) = I [3,6] ( t ), sketch the matched filter impulse response. (b) Find and sketch the convolution of s ( t ) with its matched filter. (c) Repeat (a) and (b) for s ( t ) = I [ - 1,1] ( t ) - 2 I [1,2] ( t ). (d) Based on your observations in (a)–(c), provide an intuitive justification for the following statement: A signal passed through its matched filter gives a signal that has its maximum at the origin. Problem 2: Complex exponential through LTI system (20 points) (a) Determine the output y ( t ) of a system with impulse response h ( t ) = I [ - 1,2] ( t ) when the input signal is the complex exponential x ( t ) = e j2 π f 0 t .
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