Adaptive Delta Modulation(ADM)

Adaptive Delta Modulation, a modification of Linear Delta Modulation (LDM) is a scheme that circumvents the deficiency of DM. In ADM step size Δ of the Quantizer  is not a constant but varies with time , we shall express Δ as \Delta (n)= 2 \delta (n) .

where \delta (n) increases during a steep segment of input and decreases for a slowly varying segment of input.

The adaptive step size control which forms the basis of an ADM scheme can be classified in various ways such as

  • Discrete or Continuous.
  • instantaneous (or) syllabic (fairly gradual change).
  • forward (or) backward.

we shall describe an adaptation scheme that is backward, instantaneous and discrete in practical implementation , the step size \delta (n) is constrained in between some pre-determined minimum and maximum values.

\delta _{min} \leq \delta (n)\leq \delta _{max}

The upper limit \delta _{max} controls the amount of Slope over load distortion and the lower limit \delta _{min} controls the granular noise (or) Idle noise.

The adaptive rule for  \delta (n)can be expressed in the general form \delta (n) = g(n) \delta (n-1)

where the time varying gain g(n) depends on the present binary output b(n) and M previous values b(n-1),b(n-2) ……….b(n-M). The algorithm is usually initiated with \delta _{min}.

when M=1, b(n) and b(n-1) are compared to detect probable slope over load {b(n) = b(n-1)} (or) probable granularity  {b(n) ≠ b(n-1)} then g(n) is 

  • g(n) = P if     b(n) =b(n-1).
  • g(n)=\frac{1}{P} if   b(n) \neq b(n-1).

when b(n) =b(n-1) Slope overload distortion is detected and when b(n) \neq b(n-1) Idle noise is detected.

where P\geq 1, note that P=1 represents LDM. P_{optimum}=1.5 minimizes the Quantization noise for speech signal, where 1< P< 2 is for broad class of signals.

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Author: Lakshmi Prasanna

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.