HW 08 - = c = 5 rad/s and check if the result reproduces...

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ME360 homework assignments, Spring 2010 HW8, April 2, due Friday, April 9 Reading Text 1 - 6.1 - 6.6, 6.8, 7.1, 8.6, 9.1, 9.2.0, 9.2.1, 9.2.4, 9.2.6, Table 9.2, 9.3, 9.4, 9.6.3, 13.0, 13.1, 13.2, 13.3 intro., 13.3.1, 13.3.2, 13.4 intro., 13.4.1, 13.4.2, 13.5-intro., 13.5.1,13.5.2, 13.6intro., 13.6.1, 13.6.2, 13.7 intro, 13.7.1, 13.7.2, 13.7.3, 16.7. Text 3- Ch. 9. Handout. Problems 1) Derive 1 st , 2 nd , and 3 rd order Butterworth denominator polynomials for = c = 5 rad/s. Find the poles of the polynomials for each case, draw s-plane map with pole location for each case, comment on the distribution of poles in the s-plane. Plot the magnitude spectral densities of the corresponding three low pass filters on the same graph and comment on their relative filtering properties. Plot the phase responses of these three filters on the same graph and comment on their relative phase distortion. 2) Using MATLAB function “butter” in Signal Processing Toolbox, design 1 st , 2 nd , and 3 rd order Butterworth low pass filters for
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Unformatted text preview: = c = 5 rad/s and check if the result reproduces the filters calculated in 1). 3) Implement all three filters in state-variable form in SIMULINK. Pass through each filter the sawtooth waveform (generated by the sawtooth function in the Signal Processing Toolbox) with the period T=1 sec. given by t, 0 t 1, and plot the resulting output waveforms (in the time domain, one underneath the other). 4) For each output waveform, calculate (analytically) the single-sided magnitudes of the two harmonics adjacent to the filter cut-off frequency - one to the left and the other to the right, and plot the single-sided magnitudes of these harmonics on the same graph as the function of the filter order. Indicate if the changes in the magnitudes of these harmonics as a function of filter order in the frequency domain are visible on the time domain graphs of the filter output waveforms. 5) Implement the first two filters in the state-variable scheme using inverting op amps....
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