# HW 09 - ME360 homework assignments Spring 2010 HW9 April 9...

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ME360 homework assignments, Spring 2010. HW9, April 9, due Monday, April 19 Reading Text 1 –3.7, 6.1 - 6.4, 6.8, 6.10, 7.1, 7.9, 9.1, 9.2.0, 9.2.1, 9.2.3, 9.2.4, 9.2.5, 9.2.6, Table 9.2 (convolution, conjugation, correlation, autocorrelation), 9.3, 9.4, 9.5, 9.6.3, 16.6, 16.7.4, 16.9. Text 3- Ch. 9. Problems 1. For signals x(t)=4 rect(t+3) and h(t)=(t+1) rect(t-1), find a) the autocorrelation r xx (t), b) the autocorrelation r hh (t), c) the crosscorrelation r hx (t), d) the crosscorrelation r xh (t). e) How are r hx (t) and r xh (t)related? 2. Find the Fourier transform X(f) and sketch the magnitude and phase spectra X(f) and X(f), respectively, for a) x(t)= 8-2cos(8 π t)+7sin(19 π t), b) x(t)=2 Σδ (t-6k), c) x(t)= 3sin(6 π t) . 3. Sketch the PSD (power spectral density) of x(t)=8+9sin(4 π t- π /5)-6cos(8 π t). 4. Consider a sawtooth waveform x p (t) of project 1 with period T=4, and x p (t)= 2t, 0 t 4. a) Derive the autocorrelation function of this waveform in time domain, give the time domain analytical expression of this autocorrelation function, and draw it as a function of time.
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