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General Asylum General audio topics that don't fit into specific categories. |
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General Asylum General audio topics that don't fit into specific categories. |
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In Reply to: I did some reading posted by Tre' on October 8, 2015 at 15:22:39:
Let me give you the long answer.The analog signal that you are sampling contains the musical signal S(t) plus an analog error signal consisting of distortion D(t) plus noise N(t). Digital sampling without dither turns this into sequence of quantized sample values x(i) which encode the analog signal plus error value (S+D+N) at time t(i) along with the addition of a second error signal Q(i). The quantization error Q is the difference between the value of S+D+N and the nearest digitally representable signal level. So x(i) = S(t(i)) + D(t(i)) + N(t(i)) + Q(i).
Because Q is a residual of rounding the sum of S+D+N to the nearest digital value, it is correlated to the sum of S+D+N. The spectrum of Q will depend on the spectra of those components and on how well it correlates with each of those S,D,N components, which in turn depends on the level of those components relative to Q. For example, if S>D>N>Q or S>N>Q>D, then Q will be mainly correlated with N and will have a noise-like spectrum. Since it's lower in level than N, it's buried in the analog noise floor and you can consider the sampling process to be effectively transparent. On the other hand, if S>Q>D>N or S>Q>N>D, then Q will be mainly correlated to the signal S. In that case, it will be a type of distortion whose spectrum is a function of the signal and the sampling rate. Since it is also above the analog noise floor N, the sampling process cannot be considered transparent.
For 16-bit sampling, Q is at the -96 dB level, which may be above or below the analog noise floor depending on the nature of the input signal (tape, mic feed, MIDI, etc.) So there are cases involving low noise input sources where 16-bit sampling without dithering can produce a spectrum of distortion products that many people agree is audible and everyone agrees is undesirable.
Dithering in analog to digital conversion is the intentional mixing of a pseudo-random analog signal into the input of the sampler at a level slightly above Q. So x(i) = S(t(i)) + D(t(i)) + N(t(i)) + dither(t) + Q(i). A typical dither signal used in audio is at the level of +/- 1 LSB and has a triangle PDF. It has a flat white-noise like spectrum. It's level is 3 dB above Q, so Q will end up being correlated with the dither rather than the signal, and therefore Q will have a white-noise like spectrum. The tradeoff is slightly more noise but no added distortion.
A second benefit of dithering is that periodic signals which are below the quantization noise floor are preserved in the sampled data and can extracted by time averaging. Without dithering, in the cases where Q>N, those signals are turned into distortion by the quantization process and lost.
For 24-bit sampling, Q is at the -144 dB level, which is pretty much guaranteed to be below the analog noise floor of any current recording equipment. So dithering is optional in a 24-bit ADC but it is usually done anyway. However, if you take 24-bit data and reduce it to 16-bits to fit on a CD, you still need to dither (in a digital form) to avoid introducing distortion. More generally, any process that results in a reduction in bit depth should also include dithering. Many operations performed in the digital domain by a mixing or mastering engineer require multiplication of digital values, a process which results in a longer word length than the input (e.g. multiplying two 24-bit numbers can product a result that is up to 48 bits in length). These results have to dithered rather than simply truncated or rounded to fit back into 24 bits. So most digital audio operations involve dithering of intermediate results.
To finally answer your question: With a minimalist production chain, you could conceivably record, produce, and release at 24-bits with no dither used at all. But the more processing you perform, the greater the likelihood of some quantization distortion reaching an audible level. Which is one of the reasons why dithering is a de facto standard in modern digital audio regardless of the end user delivery format.
Edits: 10/09/15
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Follow Ups
- RE: I did some reading - Dave_K 10:09:39 10/09/15 (4)
- Thank you Dave and to everyone else, please ignore most of what I've said. - Tre' 17:12:38 10/09/15 (3)
- Wish I knew for certain - Dave_K 05:26:11 10/11/15 (2)
- Dave, thanks for the education. (nt) - Tre' 16:43:56 10/18/15 (1)
- RE: Dave, thanks for the education. (nt) - Inmate51 09:35:36 10/20/15 (0)
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