Quantization noise is a key limitation in digital signal processing (DSP) systems, especially in ADCs, DACs, and fixed-point computations. Here's how you can measure, analyze, and reduce it:

What is Quantization Noise?
Quantization noise (or error) is the difference between the actual analog signal and its digital representation after rounding to the nearest discrete level. It behaves like additive noise in many cases.

1. Measuring Quantization Noise
A. Theoretical Noise Power
For a uniform quantizer:

Where:
Δ = Quantization step size

Thus:

Example: 12-bit ADC → SNR ≈ 74 dB

B. Simulation or Signal Analysis
Use tools like MATLAB, Python, or oscilloscope with FFT:

1. Input a sine wave to ADC
2. Measure output spectrum
3. Compute:
   
   

2. Reducing Quantization Noise
A. Increase Bit Resolution

• Most effective method
• Each extra bit improves SNR by ~6 dB
• Use a 16-bit ADC instead of 10-bit if precision is critical

B. Use Oversampling

• Sample signal at a rate much higher than Nyquist
• Spreads quantization noise across a wider bandwidth
• Apply a low-pass digital filter to remove high-frequency noise
• Then decimate (downsample) to reduce data rate

Improves effective resolution by ≈ 3 dB per doubling in sample rate

C. Noise Shaping (Delta-Sigma ADCs)

• Push quantization noise to higher frequencies
• Works with oversampling + digital filtering
• Used in audio ADCs and high-resolution measurements

D. Dithering

• Add small random noise before quantization
• Makes quantization error less correlated with input
• Improves subjective quality (e.g., in audio/image) and SNR in some cases

python

quantized = round(x + np.random.uniform(-Δ/2, Δ/2))  # simple dither

E. Floating Point or Extended Precision

• In fixed-point DSP: avoid overflow and rounding
• Use floating-point math or Q-format optimization
• Apply guard bits or scaling where needed

3. Tools to Analyze Quantization Noise

Summary Table