Homework_8_sol

# Homework_8_sol - Spring 2010 Homework 8 CEE 291 Problem 1...

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Spring 2010 Homework 8 – CEE 291 Problem 1 Sample the continuous analog voltage, mV, using sample time increments of 0.05 sec, 0.20 sec, and 0.80 sec. Plot the continuous signal and each sampled series over 4 periods. Determine the Nyquist and aliasing frequencies. Discuss reasons for apparent differences between each discrete representation and the analog signal. Nyquist = f s /2 = 10, 2.5, 0.625 Hz Aliasing = Only the 0.625Hz signal will be aliased. As f = 2 Hz, and fs = 1.25 Hz 2-1.25 =0.75 which is less than 1.25 1.25 – 0.75 = 0.5 Hz, the aliasing frequency Problem 2 Compute the amplitude spectrum for each of the discrete signals in problem 1. Use a data set of 128 points. Discuss apparent differences among each of the spectra and the spectrum of the continuous signal. The first two spectrums sampled at 20 and 5 Hz resolve the frequency of signal well. At f s = 1.25 Hz, the signal is aliased at 0.5 Hz as found in number 1. The amplitudes of the spectrums are a little below 5 because their signal lengths were only 128 point long. The continuous maintains the 5 amplitude and looks like the Dirac delta function at 2 Hz.

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