# ps6 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing- Continuous and Discrete Fall Term 2008 Problem Set 6: The z-Transform and Linear Filters Assigned: October 23, 2008 Due: October 30, 2008 Problem 1: A linear time-invariant filter is used to process sampled data (with sampling interval T ), and is described by the the difference equation: y n = − . 5 y n − 1 + 0 . 5 u n + u n − 1 (a) Determine the transfer function H ( z ) for the system. Express H ( z ) as a ratio of polynomials in z − 1 , and also as a ratio of polynomials in z . (b) Plot the poles and zeros of H ( z ) in the z-plane. (c) Is this a stable system? (d) From H ( z ), find the system frequency response function, and show that this is an “all-pass” system, that is H ∗...
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ps6 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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