matlabex3

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http://spsc.inw.tugraz.at/courses/dspue/matlabex3.pdf 1 Signal Processing, Problem Classes MATLAB Exercises 3 z-Transform, Sampling and Reconstruction Signal Processing and Speech Communication Laboratory Institute of Communications and Wave Propagation Graz University of Technology Inffeldgasse 16c/II http://spsc.inw.tugraz.at Summer Term, 2002 Exercise 3.1: Aliasing a Sinusoid Consider the continuous-time sinusoidal signal x ( t ) = sin(2 πf 0 t + φ ) which will be sampled at a rate f s = 1 /T s to obtain a discrete-time signal x [ n ] = x ( t ) | t = nT s = sin 2 π f 0 f s n + φ ! (a) Let f 0 be 500Hz. For φ you can choose an arbitrary value. Plot the “continuous-time” signal (sampled at 100 f 0 , use plot ) and the sampled version (use stem or plot 1 ) into the same axes (same time scale). Answer, which frequency in Hz you will get if you reconstruct the sampled version. Try the following sampling rates: 1. fs=100:100:1000; take an observation interval of 20ms 2. fs=750:250:3000; take an observation interval of 10ms (b) Now let the sampling rate be fixed at f s = 8kHz and make a series of plots of the discrete- time sinusoid. Vary the frequency of the continous-time sinusoid from 32100Hz to 32475Hz in steps of 125Hz. Predict in advance whether the apparent frequency will be increasing or

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