This document discusses delta modulation and adaptive delta modulation techniques for analogue to digital conversion. Delta modulation encodes the difference between the input signal and a reference signal into a single bit per sample, creating a staircase-like approximation of the original signal. Adaptive delta modulation varies the step size according to the input signal level to prevent slope overload. Differential pulse code modulation encodes the difference between the current and predicted sample values, sending this difference value instead of absolute sample amplitudes.

1. TELE3113 Analogue and Digital
Communications – Delta Modulation
Wei Zhang
w.zhang@unsw.edu.au
School of Electrical Engineering and Telecommunications
The University of New South Wales
TELE3113 - ∆ Modulation 23 Sept 2009 p. -1

2. Delta Modulation (1)
The difference signal is encoded into just a single bit (only two levels, +∆ and –∆).
∞
one bit per sampled point
DM transmitter ∑ δ (t − nTs )
n = −∞
ε (t )
+
-
DM signal xDM (t )
 ∆ d(t) > 0
ε (t ) = ∆ sgn[d (t )] = 
− ∆ d (t ) < 0
∞ ∞
xDM (t ) = ∆ sgn[d (t )] ∑ δ (t − nTs ) = ∆ ∑ sgn[d (nTs )]δ (t − nTs )
n = −∞ n = −∞
∞
~ (t ) =
xq ∑ ∆ sgn[d (nT )]
n = −∞
s (staircase approximation of x(t))
TELE3113 – ∆ Modulation 23 Sept 2009 p. -2

3. Delta Modulation (2)
DM signal xDM (t )
Demodulation:
Integrator + LPF
Quantization error/noise:
We assume that the quantization error eq(t) in delta modulation is
equally likely to lie anywhere in the interval (-∆,∆), then
∆
1 ∆2
2∆ −∫
e (t ) =
2
q eq (t )deq =
2
∆
3
TELE3113 – ∆ Modulation 23 Sept 2009 p. -3

4. Delta Modulation (3)
Slope overload:
d(t)
∆ dx(t )
To avoid slope overload, we require >
Ts dt max
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5. Adaptive Delta Modulation (1)
To resolve the problem of slope overload, the step size is varied according to
the level of the input signal (to catch up the change of the input signal x(t)).
If a sequence of DM pulses of the same polarity is generated (i.e. x(t)
changes rapidly and slope-overload occurs), then the step size ∆ will be
increased; if the polarity of the DM pulses tends to alternate, then the step
size ∆ will be reduced;
ADM transmitter
Integrator
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6. Adaptive Delta Modulation (2)
Demodulation: Integrator
Received ADM +LPF Recovered
signal signal
Received ADM signal
To get the relative change Recovered
envelope in step size ∆, the signal xr(t)
information will be used to
adjust the amplifier
Application: Vocoder (1.2-2.4kbit/s)
If the step size is changed continuously instead of discrete levels, it is
called continuously variable slope delta modulation (CVSDM).
TELE3113 – ∆ Modulation 23 Sept 2009 p. -6

7. Differential Pulse Code Modulation (DPCM)
~
Input message x∆ (kTs ) d (kTs ) = x∆ (kTs ) − x∆ (kTs ) DPCM signal
signal +
x(t ) Sampler Quantizer Encoder
-
~ (kT )
x∆ s Delay
~ (kT ) = ~ ((k − 1)T ) + d ((k − 1)T )
x∆ s x∆ s s
Received Recovered
d (kTs ) signal
DPCM signal Reconstruction
Decoder filter
~ (kT )
xq s
Delay
~ (kT ) = ~ ((k − 1)T ) + d ((k − 1)T )
xq s xq s s
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