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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2008 Problem Set #5 Assigned: Week of 16-Jun-08 Due Date: 23/24-Jun-08 = Please check the “Announcements” section on T-square often. All official course announcements are posted there. ALL of the STARRED problems will have to be turned in for grading. A solution will be posted to the web. Your homework is due in recitation at the beginning of class. After the beginning of your assigned recitation time, the homework is considered late and will be given a zero. PROBLEM 5.1 *: Suppose a particular linear time-invariant system is described by the difference equation y [ n ] = 3 x [ n ] + x [ n - 2] - 2 x [ n - 3] . (a) (2 pts) 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) (1 pt) This system is a causal FIR filter. Determine the filter coefficients { b k } . (c) (7 pts) Suppose the input to this system is x [ n ] = 0 for n < 0 n + 1 for n = 0 , 1 - n for n = 2 , 3 3 for n 4 Compute the values of y [ n ], over the range 0 n 12. Perform the computations by drawing up a “convolution table.” You will probably find it easiest to make a table with three rows that you need to sum. Make stem plots of both x [ n ] and y [ n ]. PROBLEM 5.2 : Which ever way you set up the convolution table in Problem 5.1(c), set it up the other way, and make sure you get the same answer.
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PROBLEM 5.3 *: The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system.
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