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# quiz1 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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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 .

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term, 2008 Quiz #1 October 16, 2008 Notes: The quiz is closed-book, two sheets of notes are allowed. The time allowed is ninety minutes. There are 4 problems, answer them all. Partial credit will be given. Some possibly useful information is given at the back of this quiz. 1
Problem 1: (20 points) A low-pass filter is to be designed from the power frequency response function 1 2 | H ( j Ω) | = 1 + Ω 4 (a) Determine a stable system transfer function based on this specification. (b) Make a pole-zero plot for the system and determine the filter class (low-pass, etc). (c) What type of design is this (Butterworth, Chebyshev Type I, etc). (d) Transform your filter design to a new filter H 1 ( s ), using the substitution 2 s s 2 + 4 −→ s in H ( s ). (e) How many poles and zeros does H 1 ( s ) have, and what class of filter (low-pass etc) is it?. Problem 2: (20 points) Your advisor (who should remain nameless!) went out and bought you a new lab computer complete with A/D converters that will sample up to 10,000 samples/second. Without consulting you he also went and bought a pressure sensor that produces a sinusoidal output with a frequency that is proportional to pressure, in the range 0 to 7 kHz. He

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