Tele3113 wk9wed
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23 Sept 2009 TELE3113 - ∆ Modulation p. -1 TELE3113 Analogue and Digital Communications – Delta Modulation Wei Zhang [email protected] School of Electrical Engineering and Telecommunications The University of New South Wales
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Transcript of Tele3113 wk9wed
23 Sept 2009TELE3113 - ∆ Modulation p. -1
TELE3113 Analogue and Digital Communications – Delta Modulation
School of Electrical Engineering and TelecommunicationsThe University of New South Wales
23 Sept 2009TELE3113 – ∆ Modulation p. -2
Delta Modulation (1)The difference signal is encoded into just a single bit (only two levels, +∆ and –∆).
DM signal
[ ]
<>
∆−∆
=∆=0)(0
)(sgn)(td
d(t)tdtε
[ ] [ ]∑∑∞
−∞=
∞
−∞=
−∆=−∆=n
ssn
sDM nTtnTdnTttdtx )()(sgn)()(sgn)( δδ
[ ]∑∞
−∞=
∆=n
sq nTdtx )(sgn)(~
)(txDM
(staircase approximation of x(t))
one bit per sampled point
)(tε
∑∞
−∞=
−n
snTt )(δ
+-
DM transmitter
23 Sept 2009TELE3113 – ∆ Modulation p. -3
Delta Modulation (2)
Demodulation: DM signal )(txDM
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
3)(
21)(
222 ∆
=∆
= ∫∆
∆−qqq detete
23 Sept 2009TELE3113 – ∆ Modulation p. -4
Delta Modulation (3)
d(t)
Slope overload:
To avoid slope overload, we requiremax
)(dttdx
Ts>
∆
23 Sept 2009TELE3113 – ∆ Modulation p. -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;
Integrator
ADM transmitter
23 Sept 2009TELE3113 – ∆ Modulation p. -6
Adaptive Delta Modulation (2)
Demodulation:
Received ADM signal
Integrator +LPF
To get the relative change envelope in step size ∆, the information will be used to adjust the amplifier
Recovered signal
Received ADM signal
Recovered signal xr(t)
If the step size is changed continuously instead of discrete levels, it is called continuously variable slope delta modulation (CVSDM).
Application: Vocoder (1.2-2.4kbit/s)
23 Sept 2009TELE3113 – ∆ Modulation p. -7
Differential Pulse Code Modulation (DPCM)
Quantizer
Delay
Input message signal
)(~skTx∆
)( skTx∆ DPCM signal
Encoder
)(~)()( sss kTxkTxkTd ∆∆ −=
Decoder
Delay
Received DPCM signal
)(~sq kTx
)( skTdRecovered
signalReconstruction
filter
Sampler)(tx+
-
))1(())1((~)(~sss TkdTkxkTx −+−= ∆∆
))1(())1((~)(~ssqsq TkdTkxkTx −+−=
