Delta Modulation Study Guide

1. Introduction to Delta Modulation

Delta Modulation (DM) is a simple analog-to-digital conversion technique that encodes the difference (delta) between consecutive samples using 1-bit quantization.

Key Characteristics:

1-bit per sample (binary output: +1 or -1)
Lower bit rate than PCM
Simple hardware implementation
Used in voice coding, military communications

Figure 1. Delta Modulation Principle

2. Working Principle

Encoder Operation

Compares current sample with predicted (staircase) value
Outputs:
b[n] = +1 if x[n] > x̂[n-1] (step up) b[n] = -1 if x[n] < x̂[n-1] (step down)

Example: For input samples [1.2, 1.5, 1.3, 1.6] and Δ = 0.2:

Encoded bits: [+1, +1, -1, +1]

Reconstructed: [1.0, 1.2, 1.4, 1.2, 1.4]

3. Receiver Operation

4. Noise in Delta Modulation Systems

Delta modulation has two main types of noise, i.e slope overload distortion and granularity.

a) Slope overload occurs when the input signal changes too rapidly for the delta modulator to follow, resulting in a distorted approximation.

b) Granularity arises when the input signal changes too slowly, causing the modulator to oscillate between its two quantization levels, producing unwanted noise.

5. Mathematical Analysis

Slope Overload Condition:

ΔT ≥ max |dx(t)/dt|

Where: Δ = step size, T = sampling interval

Signal-to-Noise Ratio (SNR)

SNR ≈ 6.02n + 1.76 dB (where n = effective bits, typically low for DM)

Granular Noise

Occurs when Δ is too small for small signal variations.

4. Adaptive Delta Modulation (ADM)

To mitigate noise in Delta modulation, adaptive delta modulation (ADM) was developed. ADM dynamically adjusts the step size based on the input signal's characteristics, allowing it to better track both rapid changes and gradual variations, thus reducing both slope overload and granular noise.

The primary goal is to dynamically adjust step size (Δ) to increase Δ during steep signal slopes (prevent overload) and to decrease Δ for small variations (reduce granular noise)

Types of ADM

Type	Description
Continuously Variable Slope Delta Modulation (CVSD)	Δ changes continuously based on signal slope
Step-Dela Modulation	Δ changes in discrete steps

Feature	DM	PCM	DPCM
Bits/sample	1	8-16	2-4
Complexity	Low	High	Medium
Quality	Low (voice only)	High	Medium

Self-Assessment Quiz

1. Why does DM use only 1 bit per sample?

Answer: It encodes only the difference (delta) between samples as +1/-1.

2. What causes slope overload distortion?

Answer: When the input signal changes faster than the staircase can follow (Δ too small).

3. How does ADM improve upon basic DM?

Answer: By dynamically adjusting step size (Δ) to match signal slope.

4. What is the main disadvantage of DM?

Answer: Poor performance for rapidly changing signals (slope overload) and granular noise.