Delta modulation (DM) is a way of digitizing a voice waveform, transmitting the digits, and reconstructing the original analog waveform that avoids the quantizer and A/D and D/A converters employed in PCM .

In linear delta modulation(LDM) the figure below determines the difference between an incoming waveform x(t) and an estimate z(t).It calculates an error voltage e(t),where  e(t) = x(t)-z(t)

and a sign quantizer determines the sign e(t).The quantizer output Q(t) is a positive constant when e(t) is positive and a negative constant when e(t) is negative . A sampling circuit samples Q(t) and generates a positive pulse when Q(t) is positive and a negative pulse when Q(t) is negative. These pulses so to a conventional PSK digital modulator for transmission.

The waveform reconstruction part of LDM receiver and the estimator portion of the modulator both use the generated pulses to form the estimate z(t) of x(t). The estimate is made by integrating the pulses and multiplying the result by a step size, ∆. If the pulses are of unit area, then the estimate z(t) increase or decreases in value at a rate equal to the sampling frequency fs if the estimate was smaller than or larger than the input waveform at the time

of the last sample. The waveforms shown below are based on a worst case assumption that the initial value of the estimate z(t) is zero.

The performance of DM system depends on the step size in two competing ways. The estimate z(t) can change by only ∆ volts at each sampling instant. If the input signal x(t) is changing more rapidly , then the estimate cannot keep up and a condition called slope overload occurs. Slope overload can be prevented by making ∆ large, but this increase granularity, the noise that results when the system hunts around a constant input value. Granularity is minimized by making ∆ small. There is an optimum step size; below it slope overload distortion dominates and above it granular noise dominates