What is Quantization?
Quantization is the process of mapping input values from a large set (often continuous) to output values in a smaller countable set. It is the core mechanism of Analog-to-Digital Conversion (ADC).
Key Definitions
- L Number of quantization levels (e.g., 8 levels = 3 bits).
- Δ Step size (Uniform Quantization). Δ = (Vmax - Vmin) / L
- e_q Quantization Error: e_q = x_q(nT_s) - x(nT_s)
Uniform Quantization Types
The placement of reconstruction levels determines the type of uniform quantizer and affects the maximum possible error.
Mid-Rise Quantizer
The origin (zero) lies in the middle of a rising part of the staircase. It does not have a zero output level.
Mid-Tread Quantizer
The origin lies in the middle of a tread (the flat part). It has a zero output level.
03 Interactive Quantization Lab
Visualize the effect of bit depth on signal quality and calculate theoretical SQNR.
Calculated Parameters
Insight
At 3 bits, the signal is barely recognizable. The error is large because the step size is significant relative to the signal amplitude.
Time Domain Analysis
Quantization Error Signal
Formula Used
Noise Analysis
Quantization error is typically modeled as a random variable with uniform distribution over the interval [-Δ/2, Δ/2].
Mean (Average Error)
E[e_q] = 0
The error is unbiased for uniform quantizers.
Variance (Noise Power)
σ² = Δ² / 12
This represents the average quantization noise power.
Probability Density Function (PDF)
The error is equally likely to be any value between -Δ/2 and +Δ/2.