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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