# quiz1_07 - MIT OpenCourseWare http:/ocw.mit.edu 2.161...

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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, 2007 Quiz #1 October 18, 2007 Notes: The quiz is open-book. The time allowed is ninety minutes. There are six problems, answer them all. Partial credit will be given. 1
Problem 1: (15 points) Show that to interpolate a value to the mid-point of a sampling interval in the sample set { f n } , n = 0 ...N 1, where f n = f ( n Δ T ), the cardinal (Whittaker) reconstructor may be written 1 N 1 f ( n Δ T + Δ T/ 2) = f k ( 1) k π ( n k + 1 / 2) k =0 Problem 2: (20 points) (a) Design (ﬁnd the transfer function of) a unity-gain 3rd-order low-pass Butterworth analog ﬁlter with a -3dB cut-oﬀ frequency of 10 rad/s. (b) Make a pole-zero plot for your ﬁlter. (c) Convert your design to a high-pass ﬁlter with the same cut-oﬀ frequency. (d) If (do not do it) you were to convert your design to a band-pass ﬁlter, what would be the order of the ﬁlter, how many zeros would be created, and where in the s -plane would the zeros lie?

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## This note was uploaded on 02/27/2012 for the course MECHANICAL 2.161 taught by Professor Derekrowell during the Fall '08 term at MIT.

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quiz1_07 - MIT OpenCourseWare http:/ocw.mit.edu 2.161...

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