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hmw3 - Due February 3 2010 BME 171 Spring 2010 HOMEWORK 3...

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Due February 3, 2010 BME 171, Spring 2010 - HOMEWORK 3 Sinusoidal Functions and Sampling 1. Given are two real analog signals x ( t ) = cos 10 πt + π 3 and y ( t ) = cos 30 t - π 4 . (a) Write formulas for corresponding complex signals ˜ x ( t ) and ˜ y ( t ) using exponen- tial notation. Identify phasors. (b) In the complex plane, sketch positions of vectors representing complex signals ˜ x ( t ) and ˜ y ( t ) at time t = 0 . 1. (c) In the complex plane, sketch position of a vector representing complex signal ˜ w ( t ) = ˜ x ( t ) + ˜ y ( t ) at time t = 0 . 1. (d) At what other time (except t = 0 . 1) will vector ˜ w ( t ) be in the same position and have the same length? 2. For this problem, please use subplots: you should turn in only one page of Matlab graphs. (a) Use Matlab function plot to plot signals x ( t ) and y ( t ) defined in Problem 1. Your plot should cover time interval from 0 to 1 s and the time vector should have sufficient number of elements so that the plots are smooth. Label the axes. (b) Use Matlab to generate two numerical sequences, x [ n ] = x ( nt s ) and y [ n ] = y ( nt s ) , that represent analog signals x ( t ) and y ( t ) sampled with the frequency of 30
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