Delta Modulation (DM)

A simple 1-bit differential coding technique, including its adaptive variants (ADM).

An Alternative to PCM: Coding the Difference

While is a universal method, other techniques exist that can be more efficient in specific applications. Delta Modulation (DM) is a prime example. Instead of coding the absolute value of each sample, DM codes the differencebetween the current sample and an approximation of the previous one. It's the simplest form of differential pulse-code modulation (DPCM), using just a single bit for quantization.

How Delta Modulation (DM) Works

The principle of DM is to track the analog input signal with a simple staircase approximation. The output is a stream of bits indicating whether the staircase should step up or step down at each sampling interval.

Delta Modulation - Encoder Block Diagram

Click a block to learn how each stage works, or use the step buttons to walk through the encoding process.

Click a block or press Next to begin

The DM Process

Comparison: The analog input signal is compared to the current value of the staircase approximation signal, which is stored in a feedback loop.
1-Bit Quantization: A simple acts as a 1-bit quantizer.
- If the input signal is greater than the approximation, the output is a binary '1'.
- If the input signal is less than the approximation, the output is a binary '0'.
Staircase Update: The binary output is fed back to an .
- Upon receiving a '1', the integrator increases its output by a fixed step size, $\delta$ .
- Upon receiving a '0', the integrator decreases its output by the same fixed step size, $\delta$ .

This process repeats at a high sampling frequency (e.g., 32 kHz), resulting in a staircase signal that "chases" the analog input and a simple binary stream representing the signal's direction of change.

Inherent Flaws: Slope Overload and Granular Noise

The simplicity of a fixed step size ( $\delta$ ) is also DM's greatest weakness, leading to two characteristic types of distortion.

Slope Overload vs. Granular Noise

Drag the step size slider to observe the fundamental trade-off in delta modulation. A small step causes slope overload on steep edges; a large step causes granular noise on flat regions.

Step size (delta)0.15

Samples60

Balanced step size -- reasonable tracking across the signal

Legend

Original signalStaircase approximationSlope overload zoneGranular noise zone

Output bitstream

101111110110101010101010101000000000000001010101010110110110

Try extreme values to clearly see each distortion type

Slope Overload Distortion

This occurs when the analog input signal changes too quickly-its slope is steeper than the staircase can follow. The fixed step size $\delta$ is too small to keep up. The result is that the approximation significantly lags behind the true signal, causing major distortion, particularly on sharp transients.

Granular Noise

This is the opposite problem. When the analog signal is relatively flat or changes very slowly, the fixed step size $\delta$ is too large. The staircase approximation constantly "hunts" above and below the signal, generating a pattern of alternating '1's and '0's. This oscillation introduces a noisy, "grainy" texture to the reconstructed signal.

The Improvement: Adaptive Delta Modulation (ADM)

To overcome the limitations of a fixed step, Adaptive Delta Modulation (ADM) was developed. In ADM, the step size is not fixed; it is dynamically adjusted based on the recent history of the output bitstream.

Adaptation Logic (Example)

To combat slope overload:If the modulator outputs a sequence of identical bits (e.g., '111' or '000'), it indicates that the approximation is failing to keep up. In response, the logic increases the step size (e.g., doubles it).
To combat granular noise:If the modulator outputs an alternating pattern (e.g., '1010'), it suggests the approximation is oscillating around the signal. The logic then decreases the step size.

This intelligent adaptation allows ADM to achieve better signal-tracking performance than standard DM, providing higher quality at the same bit rate or similar quality at a lower bit rate, with only a moderate increase in complexity.