# A9 - Signals and Systems Issued 17 October 2013 Fall 2013...

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Signals and Systems Issued: 17 October 2013 Fall 2013 Due: Friday 25 October 2013 Homework Assignment #9 1. Consider the DT, LTI system with the z -domain transfer function 2 2 ) 95 . 0 ( ) 6 / cos( ) 95 . 0 ( 2 ) ( z z z z H (a) Plot the magnitude and phase of the frequency response of the system. (b) Program the corresponding difference equation, and iterate to determine the responses to the inputs ) ( ) 12 / cos( ) ( 1 k u k k x s , ) ( ) 6 / cos( ) ( 2 k u k k x s , ) ( ) 3 / cos( ) ( 3 k u k k x s . (c) Explain the amplitudes of the steady-state responses from part (b) in terms of the system frequency response. 2. Consider the sequence x ( k ) cos( k /6). (a) Find the transfer function and the difference equation for a 2 nd -order FIR filter that has unity d.c. gain, but for which the given input x ( k ) produces zero forced response. (Your filter will have a “notch” at the given frequency, and H (1) 1.) (b) Find the transfer function and the difference equation for a stable 2 nd -order filter that has unity d.c. gain, but for which the given input

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