Delta Modulation Virtual Laboratory

Signal Parameters

Input Signal Type

Signal Frequency (f_m) 1 kHz

0.1 kHz 10 kHz

Amplitude (A_m) 1.0 V

0.1 V 3.0 V

Sampling Rate (f_s) 64 kHz

16 kHz 256 kHz

Step Size (Δ) 0.1 V

0.01 V 0.5 V

Modulation Type

Slope Condition

Δ×f_s vs 2πf_mA_m

Max Trackable Slope

6400 V/s

Δ × f_s

Signal Max Slope

6283 V/s

2πf_mA_m

Bit Rate

64 kbps

1 bit per sample

Oscilloscope View

Input

DM Output

Reconstructed

Binary Output Stream

Click "Start Animation" to generate bit stream...

+Δ (1)

-Δ (0)

System Block Diagram

Comparator + Integrator Feedback Loop

Guided Experiments

Slope Overload Observation

Observe slope overload distortion by varying signal frequency and amplitude while keeping step size constant.

Time Domain Distortion

Granular Noise Analysis

Study granular noise (idle noise) with constant or slowly varying input signals and large step sizes.

Quantization SNR

Adaptive DM Comparison

Compare Linear DM vs Adaptive DM performance under varying signal conditions.

Adaptive Comparison

Step Size Optimization

Find the optimal step size for a given signal frequency and sampling rate to minimize total distortion.

Optimization Design

Theoretical Foundation

1. Basic Principle

Delta Modulation (DM) is a differential pulse-code modulation scheme where the difference between the current sample and the previous sample is quantized using only one bit. The transmitter sends a "1" if the input signal is higher than the previous approximation, and a "0" if it is lower.

Error Signal:

e(nT_s) = m(nT_s) - m̂((n-1)T_s)

Quantized Output:

b(n) = 1 if e(nT_s) > 0, else 0

m̂(nT_s) = m̂((n-1)T_s) ± Δ

2. Slope Overload Distortion

Occurs when the maximum slope of the input signal exceeds the maximum slope that the DM system can track (Δ/T_s). The staircase approximation cannot keep up with rapid signal changes.

Condition to Avoid Slope Overload:

|dm(t)/dt|_max ≤ Δ·f_s

For Sinusoidal m(t) = A_mcos(2πf_mt):

2πf_mA_m ≤ Δ·f_s

A_m ≤ (Δ·f_s)/(2πf_m)

3. Granular Noise (Idle Noise)

Occurs when the input signal is relatively constant or changes very slowly compared to the step size. The DM output oscillates between +Δ and -Δ around the true signal value, creating a "hunting" pattern.

Granular Noise Power (approximate):

N_g ≈ Δ²/3

Signal-to-Granular-Noise Ratio:

SNR_g ≈ (3A²)/(2Δ²)

4. Adaptive Delta Modulation (ADM)

ADM dynamically adjusts the step size based on the recent history of the output bits. When consecutive identical bits are detected (indicating slope overload), the step size increases. When bits alternate (indicating granular noise), the step size decreases.

Step Size Adaptation:

Δ(n) = Δ(n-1) × K^M

Where M = 1 if b(n) = b(n-1), else M = -1

K is the adaptation constant (typically 1.5)

5. Delta-Sigma Modulation

A variation where the input signal is integrated before modulation and differentiated after demodulation. This shifts the quantization noise to higher frequencies (noise shaping) and simplifies the receiver.

Transmitter

Integrator → DM

Channel

Binary Stream

Receiver

Low-pass Filter

Performance Analysis

SNR vs Step Size

Trade-off between slope overload and granular noise

Maximum Amplitude vs Frequency

Slope overload boundary condition

Parameter Trade-offs

Parameter	Slope Overload Effect	Granular Noise Effect	Bit Rate
↑ Step Size (Δ)	Reduces	Increases	Unchanged
↑ Sampling (f_s)	Reduces	Reduces	Increases
↑ Signal Freq (f_m)	Increases	Reduces	Unchanged
↑ Amplitude (A_m)	Increases	Reduces	Unchanged

Delta Modulation Lab