Delta Modulation & Demodulation Technique
A comprehensive guide to 1-bit quantization and efficient bandwidth utilization.
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:
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:
Bit rate = Pulse rate = Sampling rate
Interactive Pulse Modulation Tool
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Explore Modulation ToolsThe 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:
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 = 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∆ - ∆ = +∆
Fig: DM Decoder at Receiver Side
Fig: Staircase Waveform Reconstruction
