Delta Modulation
The sampling rate of a signal should be higher than the Nyquist rate, to
achieve better sampling. If this sampling interval in Differential PCM is
reduced considerably, the sampleto-sample amplitude difference is very
small, as if the difference is 1-bit quantization, then the step-size will be
very small i.e., Δ (delta).
The type of modulation, where the sampling rate is much higher and in
which the stepsize after quantization is of a smaller value Δ, such a
modulation is termed as delta modulation.
Features of Delta Modulation
Following are some of the features of delta modulation.
An over-sampled input is taken to make full use of the signal correlation.
The quantization design is simple.
The input sequence is much higher than the Nyquist rate.
The quality is moderate.
The design of the modulator and the demodulator is simple.
The stair-case approximation of output waveform.
The step-size is very small, i.e., Δ (delta).
The bit rate can be decided by the user.
This involves simpler implementation.
Delta Modulation is a simplified form of DPCM technique, also viewed as 1-
bit DPCM scheme. As the sampling interval is reduced, the signal
correlation will be higher.
Delta Modulator
The Delta Modulator comprises of a 1-bit quantizer and a delay circuit along
with two summer circuits. Following is the block diagram of a delta
modulator.
The predictor circuit in DPCM is replaced by a simple delay circuit in DM.
From the above diagram, we have the notations as −
x(nTs)x(nTs) = over sampled input
ep(nTs)ep(nTs) = summer output and quantizer input
eq(nTs)eq(nTs) = quantizer output = v(nTs)v(nTs)
xˆ(nTs)x^(nTs) = output of delay circuit
u(nTs)u(nTs) = input of delay circuit
Using these notations, now we shall try to figure out the process of delta
modulation.
ep(nTs)=x(nTs)−xˆ(nTs)ep(nTs)=x(nTs)−x^(nTs)
---------equation 1
=x(nTs)−u([n−1]Ts)=x(nTs)−u([n−1]Ts)
=x(nTs)−[xˆ[[n−1]Ts]+v[[n−1]Ts]]=x(nTs)−[x^[[n−1]Ts]+v[[n−1]Ts]]
---------equation 2
Further,
v(nTs)=eq(nTs)=S.sig.[ep(nTs)]v(nTs)=eq(nTs)=S.sig.[ep(nTs)]
---------equation 3
u(nTs)=xˆ(nTs)+eq(nTs)u(nTs)=x^(nTs)+eq(nTs)
Where,
xˆ(nTs)x^(nTs) = the previous value of the delay circuit
eq(nTs)eq(nTs) = quantizer output = v(nTs)v(nTs)
Hence,
u(nTs)=u([n−1]Ts)+v(nTs)u(nTs)=u([n−1]Ts)+v(nTs)
---------equation 4
Which means,
The present input of the delay unit
= (The previous output of the delay unit) + (the present quantizer
output)
Assuming zero condition of Accumulation,
u(nTs)=S∑j=1nsig[ep(jTs)]u(nTs)=S∑j=1nsig[ep(jTs)]
Accumulated version of DM output = ∑j=1nv(jTs)∑j=1nv(jTs)
---------equation 5
Now, note that
xˆ(nTs)=u([n−1]Ts)x^(nTs)=u([n−1]Ts)
=∑j=1n−1v(jTs)=∑j=1n−1v(jTs)
---------equation 6
Delay unit output is an Accumulator output lagging by one sample.
From equations 5 & 6, we get a possible structure for the demodulator.
A Stair-case approximated waveform will be the output of the delta
modulator with the step-size as delta (Δ). The output quality of the
waveform is moderate.
Delta Demodulator
The delta demodulator comprises of a low pass filter, a summer, and a
delay circuit. The predictor circuit is eliminated here and hence no assumed
input is given to the demodulator.
Following is the diagram for delta demodulator.
From the above diagram, we have the notations as −
vˆ(nTs)v^(nTs) is the input sample
uˆ(nTs)u^(nTs) is the summer output
x¯(nTs)x¯(nTs) is the delayed output
A binary sequence will be given as an input to the demodulator. The stair-
case approximated output is given to the LPF.
Low pass filter is used for many reasons, but the prominent reason is noise
elimination for out-of-band signals. The step-size error that may occur at
the transmitter is called granular noise, which is eliminated here. If there
is no noise present, then the modulator output equals the demodulator
input.
Advantages of DM Over DPCM
1-bit quantizer
Very easy design of the modulator and the demodulator
However, there exists some noise in DM.
Slope Over load distortion (when Δ is small)
Granular noise (when Δ is large)
