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Dual-tone Multifrequency (DTMF) Signals 627
FIGURE 12.14
DTMF digits
processor), digital samples of two sine waves are generated mathematically,
scaled, and added together. The sum is logarithmically compressed
and sent to the codec for conversion to an analog signal. At an 8 kHz
sampling rate the hardware must output a sample every 125 ms. In this
case a sine look-up table is not used because the values of the sine wave
can be computed quickly without using the large amount of data memory
that a table look-up would require. For simulation and investigation
purposes, the look-up table might be a good approach in MATLAB.
At the receiving end, the logarithmically compressed, 8-bit digital
data words from the codec are received and logarithmically expanded to
their 16-bit linear format. Then the tones are detected to decide on the
transmitted digit. The detection algorithm can be a DFT implementation
using the FFT algorithm or a filter bank implementation. For the
relatively small number of tones to be detected, the filter bank implementation
is more efficient. We now describe the use of the Goertzel algorithm
to implement the 8 tuned filters.
Recall from the discussion in Chapter 5 that the DFT of an N-point
data sequence {x(n)} is
X (k) =
N−1
∑
n=0
x(n)W nk
N , k =0, 1,...,N − 1 (12.40)
If the FFT algorithm is used to perform the computation of the DFT,
the number of computations (complex multiplications and additions) is
N log 2 N.Inthis case we obtain all N values of the DFT at once. However,
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