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hw05su10 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2010 Problem Set #5 Assigned: 21-Jun-10 Due Date: 28-Jun-10 Please check the T-square chat and announcements daily. All official course announcements will be posted there. ALL of the STARRED problems should be turned in for grading. Homework is due at the start of your recitation. After this assignment is handed in by everyone, a solution to all the starred problems will be posted to the web. PROBLEM 5.1 *: Suppose a particular linear time-invariant system is described by the difference equation y [ n ] = 2 x [ n - 1] - 7 x [ n - 3] + 4 x [ n - 5] . (a) Determine the response of this system to a unit impulse input; i.e., find the output y [ n ] = h [ n ] when the input is x [ n ] = δ [ n ]. Make a stem plot of h [ n ] as a function of n . (b) This system is a causal FIR filter. Determine the filter coefficients { b k } . (c) Suppose the input to this system is x [ n ] = 0 for n < - 1 2 n for n = - 1 , 0 , 1 - n for n = 2 , 3 1 for n 4 Compute the values of y [ n ], over the range - 3 n 13. Perform the computations by drawing up a “convolution table.” You will probably find it easiest to make a table with four rows that you need to sum. Make stem plots of both
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