The Gentle Art of Dithering

Abstract

On the topic of high-performance audio, there remains disagreement over the ways in which sound quality might benefit from higher sample-rates or bit-depths in a digital path. Here we consider the hypothesis that if a digital pathway includes any unintended or undithered quantizations, then several types of errors are imprinted, whose nature will change with increased sampling rate and wordsize. Although dither methods for ameliorating quantization error have been well understood in the literature for some time, these insights are not always applied in practice. We observe that it can be rare for a performance to be captured, produced, and played back with a chain "flawless" in this regard. The paper includes an overview of digital sampling and quantization with additive, subtractive, and noise-shaped dither. The paper also discusses more advanced topics such as cascaded quantizers, fixed and floatingpoint arithmetic, and time-domain aspects of quantization errors. The paper concludes with guidelines and recommendations, including for the design of listening tests. SETTING THE SCENEIn [1] we suggested that "High Resolution" should be considered an attribute of a complete system in the analog domain (from microphone to loudspeaker)-rather than of the distributed signal or a specific technology.If the system includes a digital path, higher sample rates enable wider bandwidth and it has been questioned whether a listening preference for wider-bandwidth systems could result from the reproduction of signal frequencies above 20 kHz, or alternatively, whether it might arise as a side-effect of filtering in the chain, such as may be encountered when constraining bandwidth to meet a Nyquist criterion.In [3] and [4] we introduced a hierarchical method by which high resolution, defined as clear separation of temporal events, can be delivered efficiently. Prior to this there has been a tendency to describe resolution in the digital domain by the proxies of sample rate, bandwidth or data rate. We can't listen to a digital file without first converting it back to analog; this paper continues to consider the entire chain.A third frequency-domain hypothesis suggests that wider-band signals may cause misbehavior in playback systems (shown to be improbable in [5]).A fourth possibility, raised here, is that if a chain has defective quantizations in any part of a digital path, then the resulting errors (manifesting as distortion and/or modulation noise) also change with the inter-related variables of sampling rate and wordsize, with collateral consequences. Outline of This PaperThis paper is both a tutorial and call to action, reminding about some nowadays-overlooked fundamentals.Sec. 1 introduces the topic of modulation noise, a type of system error that can disturb or alter perception of background noise, or spatial or low-frequency elements.Sec. 2 reviews quantization distortion and in Sec. 3 we recap the properties of additive, subtractive, and noise-shaped dither, including maintaining linearity to levels well below the LSB (le...

A Hierarchical Approach for Audio Capture, Archive, and Distribution

“…8 shows a summary of the lowest spectral noise in an analysis of commercial 24-bit recordings. This noise is expressed as TPDF (triangular probability density function) dither level, i.e., the bit-depth of a triangularly dithered quantization at 192 kHz having an equivalent noise spectral density [150]. It is worth noticing that a 20-bit PCM channel is adequate to contain these recordings and consequently 32-bit precision offers no clear benefit in this regard.…”

“…When converting analog audio to a digital representation, the waveform is quantized in time and amplitude. Amplitude quantization using dither has been well described in the literature [5][6][7][8][9][10]150], while system performance consequences are previously covered in [3,21], so here we concentrate on time discretization using sampling and subsequent reconstruction to continuous time (analog). Sampling captures amplitude and timing information present in the original continuous time signal, while reconstruction presents that information in a form accessible to the ear.…”

“…13 Upper: comparing analog-to-analog frequency and impulse responses of two systems transmitting at 96 kHz, both using 3 rd -order flattening with either 2 nd -or 5 th order splines (from Table 3). Lower: comparing the 5 th order system when operated at Since in a dithered system, word-size provides a measure of dynamic range rather than of precision or resolution, with care, the word-size could be reduced for distribution with no audible impact [150].…”