HW#9 - Signals and Systems 13 October 2010 Fall 2010 Quiz...

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Signals and Systems 13 October 2010 Fall 2010 Quiz: Wednesday 20 October 2010 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 , ) ( ) ( 4 k u k x s . (c) Explain the amplitudes of the steady-state responses from part (b) in terms of the system frequency response. 2. A digital filter has the transfer function H ( z ) K ( z 2 1)( z 1) ( z 2 a 2 )( z a ) , where K is chosen so that H (1) 1. The sampling rate of the filter is T 0.000025 s. (a) Plot the frequency response magnitude of the filter for a 0, a 0.5, and a 0.9. (b) Suppose the input to the filter is given by x ( t ) cos(2  3000 t ) cos(2  10000 t ), t kT ,

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