Dithering and Noise Shaping in Digital Audio: Eliminating Quantization Distortion
Understand digital audio resolution: bit depth, quantization error, dithering, and how noise shaping reduces harmonic distortion.
Safety First: High gain settings on dither listening checks should be monitored carefully to prevent sudden loud passages when re-enabling musical audio.
Dither is a small amount of random noise added to a signal immediately before quantization, and its job is counter-intuitive: adding noise makes the conversion sound cleaner. The noise decorrelates the rounding error from the audio, converting quantization distortion into a stationary, benign hiss. Dither matters whenever bit depth is reduced, for example from a 32-bit float mix bus or 24-bit session master to 16-bit delivery, and it belongs at the end of the master chain, after every gain change, fade and limiter.
1. The Anatomy of Quantization Error
Bit depth is the number of discrete levels available per sample: 2^16 = 65,536 at 16-bit and 2^24 = 16,777,216 at 24-bit. Each step, or least significant bit, is a fixed voltage size: with full scale normalized to 1.0, the step is 2^-15 for signed 16-bit (about -90.3 dBFS) and 2^-23 for 24-bit (about -138.5 dBFS). Nothing smaller than one step can be represented directly.
Quantization rounds each sample to the nearest step, so the error depends on the input’s fractional position between steps. That is the problem. Because the error repeats with the waveform, it is correlated with the signal, and correlated error is not noise: it is harmonic distortion. On fades and reverb tails the waveform spends long stretches near the bottom codes, so the output steps and sputters. At 16 bits, a -100 dBFS reverb tail has a peak amplitude near a third of one LSB, so it is rendered almost entirely by the pattern of the last code. Rounding to nearest halves the maximum error and removes the DC offset of truncation, but not the correlation.
2. What Dither Does: Linearizing the System
Dither works by randomization: adding a random voltage before rounding makes the probability of rounding upward proportional to the signal’s fractional position. Averaged over many samples, the quantized output tracks the original waveform even when it sits between codes, and the error becomes stationary noise rather than signal-dependent distortion.
Vanderkooy and Lipshitz formalised the theory in their 1987 JAES paper, “Dither in Digital Audio”: with the right dither the nonlinear distortion term disappears and the system behaves linearly, at the cost of a slightly higher noise floor. Very low-level material survives the reduction as a statistical pattern in the noise. Two limits apply: dither cannot restore detail destroyed earlier by clipping, truncation or lossy encoding, and it cannot make a 16-bit master sound like a 24-bit one. It removes distortion, not the noise.
3. Dither Probability Densities: RPDF vs. TPDF
In the table, LSB is the step size, RMS error includes quantization, and levels are referenced to full-scale peak at 16 bits; dB figures move by 6.02 dB per extra bit of depth.
| Dither | Distribution | Span | Total RMS error | 16-bit floor |
|---|---|---|---|---|
| None | fixed | 0 | 0.289 LSB | -101.1 dBFS |
| RPDF | uniform | 1 LSB p-p | 0.408 LSB | -98.1 dBFS |
| TPDF | triangular | 2 LSB p-p | 0.500 LSB | -96.3 dBFS |
RPDF dither is one random value drawn evenly across ±0.5 LSB. It removes harmonic distortion, but the dither noise itself changes level with the signal, an artefact called noise modulation: on a fade, the hiss breathes up and down. TPDF dither is the sum of two independent uniform values, giving a triangular distribution from -1 to +1 LSB, 2 LSB peak-to-peak. It is the lowest-power dither that removes both distortion and noise modulation. The cost is measurable: TPDF raises total RMS error to half an LSB, 4.8 dB above the undithered floor and 1.8 dB above RPDF, a small constant noise floor in exchange for eliminating signal-correlated distortion.
The dither must also be scaled to the destination depth: a generator calibrated for full scale has to be attenuated to the target LSB size, or it is just loud noise. It must come immediately before the final quantization, not before a limiter that re-quantizes.
4. Psychoacoustic Noise Shaping
Noise shaping starts from TPDF and moves its energy in frequency. The quantization error runs through a feedback filter, pushing noise away from the ear’s most sensitive region, roughly 2 to 5 kHz, and up toward 15 to 20 kHz where sensitivity is far lower. A second-order shaper is enough to make an audible difference; higher orders trade more total noise for less noise in the critical band.
Shaping always increases total noise power, so a shaped 16-bit master shows a higher broadband reading than a flat-TPDF master while sounding quieter in the critical band. Shaped ultrasonic noise can excite downstream processing and become faintly audible on bright headphones.
| Depth | Levels | One LSB | Rounding floor | TPDF floor |
|---|---|---|---|---|
| 16-bit | 65,536 | -90.3 dBFS | -101.1 dBFS | -96.3 dBFS |
| 24-bit | 16,777,216 | -138.5 dBFS | -149.3 dBFS | -144.5 dBFS |
The 24-bit TPDF floor sits 48 dB below the 16-bit one, which in theory makes dither irrelevant at 24 bits, but real converters rarely reach the floor: analog noise, clock jitter and the room dominate long before -144 dBFS. Practically, 24-bit delivery makes dither inaudible, while 16-bit delivery is where shaping earns its keep.
5. When Dither Matters, and When It Does Not
Dither matters at one moment almost nobody plans for: the final reduction to a lower fixed-point depth. Dither every export whose destination is 16-bit or 24-bit, and use TPDF with shaping for 16-bit delivery when the material can spend the headroom.
It does not matter for processing that stays in float, for upconverting 16-bit to 24-bit, or for playback of a finished master where the dither is already baked in. Never dither twice on the same signal path, and never dither before a stage that will quantize again. A useful self-check: where does the next irreversible reduction happen? That is where the dither goes.
You can listen rather than trust the description: the Dithering and Noise Shaping tool runs truncation, rounding, TPDF and a shaped variant in the browser, and the Blind Bit Depth series turns the comparison into a scored test. The Spectrum Analyzer shows the shaped noise floor rising toward the top octave, and the Dynamic Range Test measures how much low-level detail changed.
6. Common Mistakes and Listening Checks
- Dithering at the wrong depth. A dither scaled for 16 bits is 48 dB above the 24-bit LSB it should match; a 24-bit dither on a 16-bit export disappears into the rounding.
- Dithering, then limiting. A limiter after the dither re-quantizes the signal and destroys the point; keep dither last.
- Auditioning at +40 dB of gain. At that gain your monitoring chain’s noise is part of the sound. Set a sane level and compare a fade with the un-dithered version.
- Shaping a bright master. Shaped noise lives in the top octave, where sibilance also lives. Audition on a neutral system before committing.