Bit Depth And Quantization
Canonical Definition
Bit depth is the nominal number of binary digits used to represent or transport each sample word. Quantization maps a continuous or higher-precision value to one of the available discrete levels. Nominal word length, meaningful signal bits, internal arithmetic precision, converter effective number of bits, and analog dynamic range are related but different quantities.
Five Different Numbers That Get Called “Bits”
| Quantity | Example | What it means |
|---|---|---|
| File or stream word length | 24-bit PCM | Container or transported sample width |
| Serial slot width | 32-bit slot | Clocked space reserved for the word |
| Meaningful source precision | 16 valid bits inside 24 | Actual nonzero or useful source detail |
| DSP arithmetic precision | 28-bit core, 56-bit accumulator | Internal calculation and headroom format |
| Converter effective resolution | measured ENOB or noise floor | Performance after analog noise and distortion |
Quantizer Outcomes
- Rounding: chooses the nearest representable value.
- Truncation: discards lower-order information in a defined direction or format.
- Saturation: holds at the maximum or minimum representable value.
- Wraparound: overflows into the opposite numeric range and can create severe distortion.
- Dithered reduction: adds controlled noise before quantization so the error is decorrelated.
Serial Alignment Matters
A 24-bit sample may occupy a 24- or 32-bit slot. I2S, left-justified, and right-justified interfaces position the word differently relative to the frame edge. The wrong justification or one-bit delay can turn a valid stream into near-full-scale noise even when the clocks appear correct.
ADAU1701 Context
The ADAU1701 extends normal input data into its 28-bit core and uses wider accumulation for many calculations. That internal headroom does not make the ADCs, DACs, serial outputs, or external analog stages unlimited. Document the numeric format and every point where a value returns to a narrower boundary.
Verification
- Record word length, slot width, justification, signedness, and fixed-point format.
- Test silence and a low-level tone before full-scale signals.
- Measure noise floor and low-level linearity instead of inferring performance from the label.
- Identify every rounding, truncation, saturation, and dither stage.
- Confirm the final converter and analog limits separately.