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# comp2 - EEE 391 Basics of Signals and Systems Computer...

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EEE 391 Basics of Signals and Systems Computer Assignment II Due: 4 November 2011, Friday by 17:00 in the homework box Consider the following periodic waveforms: i) a square wave with period T , duty cycle 40%, and average value 2, ii) a triangular waveform with period T and average value –1, iii) a sawtooth waveform with period T and average value zero, iv) a half-wave rectified sine function with period T and average value –2. a) Sketch these waveforms as accurately as possible and label them as needed. b) Find all of the Fourier series coefficients of these waveforms through analysis by hand and express them as compactly as possible. c) If all of the Fourier series coefficients are used, the synthesis equation is as follows: x ( t ) = summationdisplay k = −∞ a k e j 2 πkf t where f = 1 /T is the fundamental frequency of the waveform. However, infinite limits are not practical when trying to synthesize the signal on a computer. Try to approximate the periodic signal x ( t ) by truncating the synthesis equation using different values of
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