Selected Topics in Applied Signal Processing - Digital Signal Processing: An Introduction with MATLAB and Applications - page 170

difference between the current sample and the previous sample; with such an
approach, a smaller number of bits is required for encoding. The disadvantage of
using this type of differential quantization is that a memory is needed to maintain
knowledge of the previous sample. A slightly different approach involves com-
paring the current sample to its predicted value (determined from previous sam-
ples) rather than the previous sample, then encoding the difference. The encoding
here is called differential PCM (DPCM). The disadvantage of DPCM is that it
needs a feedback loop and associated memory.
One way to achieve DPCM is the delta modulation (DM) system shown in
Fig. 3.31 . This DM is a first-order analog feedback system that consists of a
quantizer clocked at the sampling rate f s and an integrator (I). The integrator does a
linear prediction x ð n Þ of the current sample x(n), based on the previous sample
x(n - 1) and the most recent error. The quantized output is a comparator that
gives either 1 (logic-1) if x ð n Þ x ð n Þ and -1 (logic-0) if x ð n Þ \x ð n Þ: Only a 1-bit
word is needed for encoding, since the output is either logic-0 or logic-1. The
integrator has a scaling factor D ; which is referred to as the step-size.
The operation of the DM can be further explored with an example. Consider the
input analog signal shown as a dotted curve in Fig. 3.32 . tisx ð t Þ¼
0 : 8 sin ½ 2p ð 0 : 1 Þ t þ 0 : 1 volt. The sampling frequency is f s = 10 Hz (i.e., T s = 0.1

Clock ( f s )

e ( t )

1
−1

∼ x ( t )

x ( t ) y ( t ) Δ ∫ LPF

−1
Quantizer
Integrator

^
x ( t ) [ DM Decoder ]

Δ ∫ y(t).dt

[ estimate of x ( t ) ]

[ DM Encoder ]

Fig. 3.31 Delta modulator and demodulator

T s

1

kT s

−1

k 0 1 2 3 4 5 30

Fig. 3.32 Delta modulation waveforms