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ps3 - inequality Problem 2(Complex exponential through LTI...

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UCSB Fall 2007 ECE 130A: Problem Set 3 Assigned: Monday, October 15 Due: Tuesday, October 23 Reading: 2.2, 2.3, 3.3, 3.5 Optional additional reading: 3.4 (for people interested in theoretical issues) Midterm reminder: Monday October 29, in class Problem 1 (Matched filter): 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 computations, try to provide an intuitive justification for the following statement: a signal passed through its matched filter always gives a peak at the origin. (e) Bonus problem: Prove the statement in (d) by looking up and applying the Cauchy-Schwartz
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Unformatted text preview: inequality. Problem 2 (Complex exponential through LTI system): Find the output y ( t ) when you pass the complex exponential signal s ( t ) = e j 2 πf t through a ±lter with impulse response h ( t ) = I [-1 , 3] ( t ). Assuming that the unit of time is microseconds, at what values of f (in KHz) is the output identically zero? Problem 3 (Find signal given Fourier series coe±cients): 3.21 Problem 4 (Find Fourier series coe±cients given sinusoidal signal): 3.3 Problem 5 (Find Fourier series coe±cients given general periodic signal): (a) Signal in Figure P3.22(a) (b) Signal in Figure P3.22(d) (c) 3.22(c)...
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