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Sec. 3–7 Differential Pulse Code Modulation 195
y(nTs)
Delay
Ts
a 1
Delay
Ts
•
••
•
••
•
••
•
••
Delay
Ts
a 2 a l a K
•
••
z(nTs)
Figure 3–28
Transversal filter.
receiver, the present sample value is regenerated by using the past value plus the update differential
value that is received over the differential system.
Moreover, the present value can be estimated from the past values by using a
prediction filter. Such a filter may be realized by using a tapped delay line (a bucket
brigade device) to form a transversal filter, as shown in Fig. 3–28. When the tap gains {a l }
are set so that the filter output will predict the present value from past values, the filter is
said to be a linear prediction filter [Spilker, 1977]. The optimum tap gains are a function
of the correlation properties of the audio or video signal [Jayant and Noll, 1984]. The output
samples are
or, in simplified notation,
K
z(nT s ) = a a l y(nT s - lT s )
l=1
K
z n = a a 1 y n - l
l=1
(3–79a)
(3–79b)
where y n - l denotes the sample value at the filter input at time t = (n - l)T s and there are
K delay devices in the transversal filter.
The linear prediction filter may be used in a differential configuration to produce
DPCM. Two possible configurations will be examined.
The first DPCM configuration, shown in Fig. 3–29, uses the predictor to obtain a differential
pulse amplitude-modulated (DPAM) signal that is quantized and encoded to produce
the DPCM signal. The recovered analog signal at the receiver output will be the same as that
at the system input, plus accumulated quantizing noise. We may eliminate the accumulation
effect by using the transmitter configuration of Fig. 3–30.