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:
4915877
(Toscanini’s Ice
Cream Shop in Cambridge, MA) and
2531000
(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:
5342230
(UCSD) and
5500406
(Regents Pizzeria). These are places
frequented by your Professor!
In this lab assignment, you’ll use the DTFT to analyze touchtone 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 frequencydomain spectrum, then, should be sinusoidal peaks (deltafunctions)
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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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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 Spring '09
 Telephone exchange, Telephone number, Phone Number, Fast Fourier transform

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