Exercises for Chaos Under Control

Chapter 6: Prisms, Pianos, and Spectral Analysis

1. The lower left graph shows the power spectrum of the signal displayed in part (a) of that figure. Sketch the power spectra of the signals shown in parts (b) and (c). Answer

2. In the upper right graph we see the power spectrum of the signal in (a). Sketch the signals for the power spectra (b) and (c) shown in the figure.

3.[N] Suppose S1(t) is a sine wave of amplitude 5 and period 60 seconds, S2(t) is a sine wave of amplitude 2 and period 30 seconds and S3(t) is a sine wave of amplitude 1 and period 20 seconds. Suppose also that all three are zero at t = 0 and start to increase as t begins to increase from 0. What is the amplitude of the composite wave S1(t) + S2(t) + S3(t) at

(a) t = 60 seconds, Answer

(b) t = 30 seconds, Answer

(c) t = 15 seconds. Answer

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