lab_solution6

# lab_solution6 - ECE 101 Linear Systems Fundamentals Fall...

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ECE 101 – Linear Systems Fundamentals, Fall 2009 Lab # 6 Solutions December 1, 2009 (send questions/comments to [email protected]) NOTE: These solutions demonstrate the decoding of the telephone numbers: 491-5877 (Toscanini’s Ice Cream Shop in Cambridge, MA) and 253-1000 (MIT, also in Cambridge, MA). These places were frequented, no doubt, by the authors of the “Computer Explorations” book. The phone numbers that you decoded were local ones: 534-2230 (UCSD) and 550-0406 (Regents Pizzeria). These are places frequented by your Professor! 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:

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(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. Below are plots of the magnitude responses of the DTFTs of d
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lab_solution6 - ECE 101 Linear Systems Fundamentals Fall...

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