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Unformatted text preview: MAE107 Homework #5 Prof. MCloskey Due Date The homework is due at 5PM on Tuesday, May 25, 2010, to David Shatto (38138 foyer, Engineer ing 4). Reading Please read the introduction to Chapter 17 and sections 17.1 thru 17.7. This material covers the bilateral and unilateral Laplace transform. Problem 1 This problem discusses correlation functions and their relation to inputoutput signals of linear systems. Consider the lowpass filter described by the differential equation V out + 1 RC V out = 1 RC V in . For the sake of brevity, define = 1 / ( RC ). Thus, the impulse response of the circuit is h ( t ) = e t ( t ) . Let the input to the circuit be V in ( t ) = ce ct ( t ) , c > . (1) In this problem, we dont consider the limit as c the input is chosen to be this form because it makes the computations easier to carry out. Answer the following: 1. Compute V out given the input (1). Note that time is defined on ( , ). 2. Compute the autocorrelation of (1). In other words, compute a new function of time given by R V in V in ( t ) = Z  V in ( t + ) V in ( ) d, t ( , ) . You will need to consider the two cases when t < 0 and t 0. 3. Compute the crosscorrelation , R V out V in , where V in is given by (1) and V out is the output calculated in part 1: R V out V in ( t ) = Z  V out ( t + ) V in ( ) d....
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 Spring '06
 TSAO

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