MAS160: Signals, Systems & Information for Media TechnologyProblem Set 6DUE: November 12, 2003Instructors: V. Michael Bove, Jr. and Rosalind Picard T.A. Jim McBrideProblem 1: Frequency response of FIR filters (DSP First 6.4)Problem 2: Simple sound filteringUsing our old friend the sumcos function, create a sound with a fundamental frequencyof 440 Hz, with 12 harmonics of equal amplitude and zero phase, and using the followingparameters:fs = 11025; % Sets sampling rate to 11025 Hzf = 440*[1:12]; % Creates frequency vector of 12 harmonics of 440 HzX = ones(1,12); % Creates amplitudes of 1dur = 1; % Sets duration to be 1 secUse MATLAB to perform the following tasks:(a) Create a three-point averaging FIR filter and plot the frequency response (magnitudeand phase) of this filter using freqz. What is this filter supposed to do? Filter thesound you created above with this filter. How does it compare to the original sound?(b) Create a two-point first difference FIR filter and plot the frequency response (magni-tude and phase) of this filter using freqz. What is this filter supposed to do? Filterthe original sound you created above using this new filter. How does it compare tothe original sound?Problem 3: Return of the Labs: DSP First Lab 5Items to be turned in:(a) Plots and answers to questions specified in C.5.2.1.(b) Plots and answers to questions specified in C.5.3.2.(c) Demonstrate linearity and time-invariance of filter (C.5.3.3 and C.5.3.4).(d) Plots and answers to questions specified in C.5.3.5.PS 6-1Problem 4: Additional Problem (for MAS.510)The matlab function zplane is great for plotting the poles and zeros of a system in thez-plane. Use zplane as well as freqz to answer the following questions.(a) Consider the general N -point FIR averaging filter, where each coefficient bkis simply1N. Plot the zeros of this system in the z-plane as well as the frequency response(magnitude and phase) for N = 3, 4, 5, and 10. How does the position of the zeroschange? Qualitatively, how does the frequency response change, and how does thisrelate to the location of the zeros? Does N being an even or odd number have anyeffect?(b) Consider the general N -point FIR difference filter, where each coefficient bkis simply(−1)kN. Plot the zeros of this system in the z-plane as well as the frequency response(magnitude and phase) for N = 3, 4, 5, and 10. How does the position of the zeroschange? Qualitatively, how does the frequency response change, and how does thisrelate to the location of the zeros? Does N being an even or odd number have anyeffect?PS
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