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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 6254 Spring 2010 Problem Set #1 Assigned: January 18, 2010 Due Date: January 26, 2010 Reading Assignment : Chapter 4, Sections 4.1  4.4.1 (pp. 129154). Quote of the Week The purpose of models is not to fit the data but to sharpen the questions. Samuel Karlin, 11th R.A. Fisher Memorial Lecture, 1983. PROBLEM 1.1: In Pad es method, we model a signal x ( n ) as the unit sample response of a filter that has a system function of the form H ( z ) = B q ( z ) A p ( z ) and the filter coefficients a p ( k ) and b q ( k ) are found so that x ( n ) = h ( n ) for n = 0 , 1 ,...,p + q . In this problem, we consider some generalizations of Pad es method. (a) One way to generalize the approach of Pad e is to consider matching x ( n ) to the unit sample response h ( n ) over other intervals. For example, instead of forcing x ( n ) = h ( n ) for n [0 ,p + q ], suppose we would like to find values for a p ( k ) and b k ( q ) so that x ( n ) = h ( n ) for n = n 1 ,n 1 + 1 ,...,n 1 + p + q , i.e. over an interval of length p + q + 1 that begins at n = n 1 rather than n = 0. Is this possible? If so, derive the equations that must be solved and work an example by defining a signal and then finding the model. If it is not possible, explain whyan example by defining a signal and then finding the model....
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 Spring '09
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