# ps3soln - 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 3 Solution: Analog Filter design Problem 1: Use the nomenclature in the class handout. For both filters: 1 1 = 0 . 5 −→ ǫ = 1 , = 0 . 1 −→ λ = 3 1 + ǫ 2 1 + λ 2 (a) For Filter A, Butterworth design: log( λ/ǫ ) log(3) N ≥ = = 2 . 71 log(Ω r / Ω c ) log(1 . 5) Therefore select N = 3 . (b) For Filter A, Chebyshev design: cosh − 1 ( λ/ǫ ) cosh − 1 (3) N ≥ = = 1 . 831 cosh − 1 (Ω r / Ω c ) cosh − 1 (1 . 5) Therefore select N = 2 . (c) For Filter B, Butterworth design: log( λ/ǫ ) log(3) N ≥ = = 6 . 81 log(Ω r / Ω c ) log(1 . 175) Therefore select N = 7 . (d) For Filter B, Chebyshev design: cosh − 1 ( λ/ǫ ) cosh − 1 (3) N ≥ = = 3 . 02 cosh − 1 (Ω r / Ω c ) cosh − 1 (1 . 175) Therefore select N = 4 . (e) % Design the filter [A,B]=butter(3,2*pi*10000,’s’); filt=tf(A,B); % Create a frequency vector w=[0:2*pi*100:2*pi*30000]; % Compute the freq resp. at the frequencies in the vector [MAG, PHASE] = bode(filt, w); % Plot the response plot(w/(2*pi), squeeze(MAG).^2); grid; xlabel(’Frequency (Hz.)’); ylabel(’Power Response’); title(’PS2- Problem 1(e)’); 1 Power Response PS2 − Problem 1(e) 1 0 0.5 1 1.5 2 2.5 3 0.8 0.6 0.4 0.2 0 Frequency (Hz.) x 10 4 (f) For the standard MATLAB functions we need to design a filter with Ω c = 1 rad/s....
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ps3soln - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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