mp1 - Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING MATLAB Mini-Project 1 Spring

mp1 - Michigan State University Department of Electrical...

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Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING MATLAB Mini-Project 1 Spring 2008 Issued: Friday, February 22, 2008 Due: Friday, February 29, 2008 1.Numerical Approximation of the Convolution Integral(Adapted from Computer Explorations in Signals and Systems UsingMATLAB, Prentice Hall, 2002.)The convolution integral represents the input-output relationship of a linear andtime-invariant system and is given as follows:y(t) =−∞f(τ)h(tτ)=f(t)h(t),where the inputf(t) and the impulse responseh(t) are causal infinite durationsignals. This integral cannot be solved exactly for the outputy(t) at any given valueoftusing a computer, because an infinite amount of memory would be needed tostoref(t) andh(t) and an infinite number of multiplication and addition operationswould be needed to perform the calculation. Moreover,y(t) could not be calculatednor approximated for all values oftusing a computer, becausettakes on acontinuum of values. However, samples ofy(t) over a finite interval of time may beapproximated using a computer according to the following steps:i) Truncatef(t) over a finite time interval and sample the truncated signal at timeintervals equal toTsto arrive atf

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