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630 Chapter 12 APPLICATIONS IN COMMUNICATIONS
filter computation) can be simplified. In particular, we have
|X(k)| 2 =|y k (N)| 2 = ∣ ∣v k (N) − W k Nv k (N − 1) ∣ ∣ 2 (12.50)
(
=v k(N)+v 2 k 2 (N − 1) − 2 cos 2πk )
v k (N)v k (N − 1)
N
Thus complex-valued arithmetic operations are completely eliminated in
the DTMF detector.
12.6.2 PROJECT 12.6: DTMF SIGNALING
The objective of this project is to gain an understanding of the DTMF
tone generation software and the DTMF decoding algorithm (the Goertzel
algorithm). Design the following MATLAB modules:
1. a tone generation function that accepts an array containing dialing
digits and produces a signal containing appropriate tones (from
Figure 12.14) of 0.5-second duration for each digit at 8 kHz sampling
frequency
2. a dial-tone generator generating samples of (350 + 440) Hz frequency
at 8 kHz sampling interval for a specified amount of duration
3. a decoding function to implement (12.50) that accepts a DTMF signal
and produces an array containing dialing digits
Generate several dialing list arrays containing a mix of digits and
dial tones. Experiment with the tone generation and detection modules
and comment on your observations. Use MATLAB’s sound generation
capabilities to listen to the tones and to observe the frequency components
of the generated tones.
12.7 BINARY DIGITAL COMMUNICATIONS
Digitized speech signals that have been encoded via PCM, ADPCM, DM,
and LPC are usually transmitted to the decoder by means of digital modulation.
A binary digital communications system employs two signal waveforms,
say s 1 (t) =s(t) and s 2 (t) =−s(t), to transmit the binary sequence
representing the speech signal. The signal waveform s(t), which is nonzero
over the interval 0 ≤ t ≤ T ,istransmitted to the receiver if the data bit is
a1,and the signal waveform −s(t), 0 ≤ t ≤ T is transmitted if the data bit
is a 0. The time interval T is called the signal interval, and the bit rate over
the channel is R =1/T bits per second. A typical signal waveform s(t) is
a rectangular pulse—that is, s(t) =A, 0≤ t ≤ T —which has energy A 2 T .
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