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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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?
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 6

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online