# ps4 - ω and φ which could give the waveform shown above...

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2.171 Problem Set 4 Assigned: Wed. Oct 4, 2006 Due: Wed. Oct 11, 2006, in class Reading: 5.1, 5.2, 6.1, 6.2, 7.1, 7.2, 7.3, Oppenheim and Wilsky Ch. 7, Notes from class Problem 1 Oppenheim and Wilsky, Problem 7.29 Problem 2 Oppenheim and Wilsky, Problem 7.31 Problem 3 The ±gure below shows a discrete-time waveform y ( k ) = y a ( kT ) which results from sampling a continuous time sinusoid y a ( t ) = sin( ωt + φ ) at sampling instants t = kT . Note that the waveform is periodic with period N = 16. 0 2 4 6 8 10 12 14 16 18 20 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 k y(k) a) What are the values of ω and φ with the smallest magnitudes which could give the waveform shown above? (These will of course depend on T.) Explain your reasoning and show the relevant calculations. b) What are all the possible values of
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Unformatted text preview: ω and φ which could give the waveform shown above? Explain your reasoning and show the relevant calculations. Problem 4 F,P, & W 5.7 Problem 5 F,P, & W 6.3 Only work the problem for the forward, backward, Tustin, and pole-zero matching approaches, i.e., only for parts i, ii, iii, and v. Do not solve for the other transformation types. Note: For this problem, let T = 0 . 015 s, rather than the sample time indicated in the problem statement. Problem 6 F,P, & W 7.3 Problem 7 F,P, & W 7.15 1...
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