Infinite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 383

x¼ 1234
>> [X1, A1]¼galg(x,1)
X1 ¼ -2.0000 þ 2.0000i
A1 ¼0.7071
b. For Example 8.27, we obtain
>> x¼[1 2 3 4]
x¼ 1234
>> [X0, A0]¼galg(x,1)
X0 ¼ 10
A0 ¼ 2.5000

8.11.4 Dual-Tone Multifrequency Tone Detection Using
the Modified Goertzel Algorithm
Based on the specified frequencies of each DTMF tone shown in Figure 8.48 and the modified Goertzel
algorithm, we can develop the following design principles for DTMF tone detection.
1. When the digitized DTMF tone xðnÞ is received, it has two nonzero frequency components from the
following seven: 697, 770, 852, 941, 1,209, 1,336, and 1,477 Hz.
2. We can apply the modified Goertzel algorithm to compute seven spectral values, which
correspond to the seven frequencies in (1). The single-sided amplitude spectrum is

computed as

q

jXðkÞj

2
N

2

A k ¼ (8.78)

3. Since the modified Goertzel algorithm is used, there is no complex algebra involved. Ideally, there
are two nonzero spectral components. We will use these two nonzero spectral
components to determine which key is pressed.
4. The frequency bin number (frequency index) can be determined based on the sampling rate
f s , and the data size of N via the following relation:

k ¼ f

f s N ð round off to an integer Þ

(8.79)

Given the key frequency specification in Table 8.12 , we can determine the frequency bin k for each
DTMF frequency with f s ¼ 8 ; 000 Hz and N ¼ 205.
The DTMF detector block diagram is shown in Figure 8.55 .
5. The threshold value can be the sum of all seven spectral values divided by a factor of 4. Note
that there are only two nonzero spectral values, hence the threshold value should ideally be half
of the individual nonzero spectral value. If the spectrum value is larger than the threshold
value, then the logic operation outputs logic 1; otherwise, it outputs logic 0. Finally, the
logic operation at the last stage is to decode the key information based on the 7-bit binary
pattern.