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Sec. 3–8 Delta Modulation 203
This result can be used to design a VF DM system. For example, suppose that we desire
an SNR of at least 30 dB. Assume that the VF bandwidth is 4 kHz and the average-to-peak audio
1
power is
2.
Then Eq. (3–89) gives a required sampling frequency of 40.7 kbitss, or f s = 10.2B.
It is also interesting to compare this DM system with a PCM system that has the same bandwidth
(i.e., bit rate). The number of bits, n, required for each PCM word is determined by
R = (2B)n = 10.2B or n ≈ 5. Then the average-signal to quantizing-noise ratio of the comparable
PCM system is 30.1 dB. (See Table 3–2.) Thus, under these conditions, the PCM system with a
comparable bandwidth has about the same SNR performance as the DM system. Furthermore,
repeating the preceding procedure, it can be shown that if an SNR larger than 30 dB were
desired, the PCM system would have a larger SNR than that of a DM system with comparable
bandwidth; on the other hand, if an SNR less than 30 dB were sufficient, the DM system would
outperform (i.e., have a larger SNR than) the PCM system of the same bandwidth. Note that the
SNR for DM increases as f 3 s, or a 9-dB-per-octave increase in f s .
It is also possible to improve the SNR performance of a DM system by using double
integration instead of single integration, as was studied here. With a double-integration system,
the SNR increases as , or 15 dB per octave [Jayant and Noll, 1984].
f 5 s
Adaptive Delta Modulation and Continuously Variable
Slope Delta Modulation
To minimize the slope overload noise while holding the granular noise at a reasonable
value, adaptive delta modulation (ADM) is used. Here the step size is varied as a function
of time as the input waveform changes. The step size is kept small to minimize the granular
noise until the slope overload noise begins to dominate. Then the step size is increased
to reduce the slope overload noise. The step size may be adapted, for example, by examining
the DM pulses at the transmitter output. When the DM pulses consist of a string of
pulses with the same polarity, the step size is increased (see Fig. 3–32) until the DM pulses
begin to alternate in polarity, then the step size is decreased, and so on. One possible
algorithm for varying the step size is shown in Table 3–7, where the step size changes with
discrete variation. Here the step size is normally set to a value when the ADM signal consists
of data with alternating 1’s and 0’s or when two successive binary 1’s or 0’s occur.
However, if three successive binary 1’s or three successive binary 0’s occur, the step size is
TABLE 3–7
STEP-SIZE ALGORITHM
Data Sequence a
Number of
Successive
Binary 1’s or 0’s
Step-Size
Algorithm,
f(d)
X X 0 1 1 δ
X 0 1 1 2 δ
0 1 1 1 3 2δ
1 1 1 1 4 4δ
a X, do not care.