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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 (38-138 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 input-output signals of linear systems. Consider the low-pass 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 auto-correlation 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 cross-correlation , 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