ECE 101 lab_solution5

ECE 101 lab_solution5 - ECE 101 Linear Systems...

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ECE 101 – Linear Systems Fundamentals, Winter 2008 Lab # 5 Solutions February 28, 2008 (send questions/comments to [email protected]) In this lab assignment, you’ll use the DTFT to analyze touch-tone telephone sounds, play your own phone number with MATLAB, and decode a couple phone numbers. When you push a key on your phone, the sound you hear is the sum of two sinusoids, y[n] = sin( ω C n) + sin( ω R n) where ω C and ω R are pair of frequencies given by the table below: The corresponding frequency-domain spectrum, then, should be sinusoidal peaks (delta-functions) centered at plus/minus the two frequency values. (a) To listen to, say, the sound of the digit 2, we can use the commands: n = 0:999; d2 = sin(0.5346*n) + sin(1.0247*n); sound(d2,8192); The digit 2 has the frequencies ω R = 0.5346 and ω C = 1.0247 associated with it, as seen from the table. A plot of the tone looks like this: (b) In MATLAB, we can use the Fast Fourier Transform, fft( ) , to approximate the DTFT of the touch- tone signal. We’ll examine the digits 2 and 9. According to the table, the digit 2 should have sinusoidal peaks at ω R = 0.5346 and ω C = 1.0247, and the digit 9 should have peaks at ω R = 0.6535 and ω C = 1.1328.
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Below are plots of the magnitude responses of the DTFTs of d 2 [n] and d 9 [n]: From the plots, we see that for the digit 2, we get delta-function peaks in the frequency domain around ω R = 0.5346 and ω C = 1.0247, and for the digit 9, we get peaks around ω R = 0.6535 and ω C = 1.1328, as expected. (c)
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This note was uploaded on 03/16/2009 for the course ECE 101 taught by Professor Siegel during the Spring '08 term at UCSD.

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ECE 101 lab_solution5 - ECE 101 Linear Systems...

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