Delta Modulation & Demodulation

Delta Modulation & Demodulation Technique

A comprehensive guide to 1-bit quantization and efficient bandwidth utilization.

Delta Modulation Demodulation MATLAB Code Other Techniques

Delta Modulation Overview

Another name for delta modulation is a 1-bit quantizer. To minimize complexity and bandwidth per sample, we use n = 1 bit/sample.

We know that bandwidth (BW) for PCM is typically calculated as:

BW = nfs / 2

Where:

n = number of bits per sample (n=1 for DM)
fs = Sampling Frequency

To ensure accuracy, DM uses a high sampling rate (fs >> 2fm), known as oversampling. This allows the 1-bit steps to track the message signal closely.

If data rate Rb = nfs, then:

Rb = fs (since n=1)

Bit rate = Pulse rate = Sampling rate

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The Modulation Process

Since we allocate 1 bit/sample, the number of levels is L = 2¹ = 2. The quantizer output is either +∆ or -∆.

We compare the current sample value to the prior approximated value. If the error is positive, the output is '1'. If the error is negative, the output is '0'.

Fig: Delta Modulation Block Diagram

Input of the quantizer:

e(nTs) = m(nTs) – m^(nTs)

Where:

m(nTs) = current sample
m^(nTs) = predicted/accumulated value

Note: If the signal changes too fast for the step size (∆), Slope Overload Distortion occurs.

Delta Demodulation

The receiver acts as an accumulator. If the incoming bit is '1', the output increases by +∆. If the bit is '0', the output decreases by -∆.

Fig: Diagram of DM Quantizer Logic

Fig: DM Encoder System

Decoding Process Logic

The staircase waveform is reconstructed by summing the steps over time:

At t = 0: initial value = 0
At t = Ts (Bit 1): 0 + ∆ = +∆
At t = 2Ts (Bit 1): +∆ + ∆ = +2∆
At t = 3Ts (Bit 1): +2∆ + ∆ = +3∆
At t = 4Ts (Bit 0): +3∆ - ∆ = +2∆
At t = 5Ts (Bit 0): +2∆ - ∆ = +∆