solderdude
Grand Contributor
signal --> adding 1LSB dither (for 16 bit) --> encoding in 16 bit.
Yes, this is in more details.signal --> adding 1LSB dither (for 16 bit) --> encoding in 16 bit.
But I'm talking here about different levels of information - engineering and semantic (you pointed to the appropriate article by Warren Weaver above). In order to understand better the difference between those levels I suggested the following example above: if you have a series of 32bit values of unknown origin and you need to convert them to 16bit values, will you apply noise before rounding? What is recommended by math in this case?
I would mostly agree here. The applied math can not be used in this case, because we don't know the application area of the signal. And the best strategy for quantizing unknown signal is rounding as it provides the best Signal-to-Quantization-Noise Ratio. There are several other quantizing methods [wiki], which can be used depending on the nature of signal and its properties (prob.distr.function). And this is the point where my reasoning of psychoacoustic nature of dithering in audio originates from.APPLIED mathematics? Without knowing more, there isn't an answer. In the case of LPCM audio applications, dither. The "noisy channel" is 16-bit LPCM, the ultimate receiver is the ear/brain system.
Agree with the one note. For Humans the meaning of sound closely relates to psychoacoustic properties of hearing. For example sensation of dissonances and consonances is determined by critical bands of hearing, which in turn are determined by mechanical properties of basilar membrane in the inner ear. So, semantics of sound includes also psychoacoustics (ear/brain). As a result we have at least two levels of audio information - engineering (without meaning) and semantic (with psychoacoustics).The "semantic" question is one of whether "white noise" constitutes "music" or not.
Applying your example to audio signals we could similarly say the following. Operating on the semantic level of audio signal (mixing, applying effects, ...) we can abstract away the engineering level only if corresponding operations on this level do not degrade the signal on the semantic level (properly coded in 32bit arithmetics). In other words, engineering level of audio information can be abstracted away only being fully transparent for semantic level.In this context, other "layers" aren't relevant... yes, one could move down the "stack" and consider a collection of 0's and 1's are that are lossless coded in FLAC and in this case the original LPCM is recovered in the FLAC decoder. Or even CD-DA...
Or the multiple layers between a software audio player (e.g. running on a PC) and a hard drive, and so on. The hard drive's own controller doesn't "care" whether the data is LPCM audio or MALWARE, its only job is to return the requested data without error, and in turn the user (i.e. the OS) doesn't "care" what the hard drive does, e.g. error correction, whether it has "quietly" reallocated sectors, etc... up to the point that it cannot return error-free data... and so on, back to the software player, which "talks" to the OS at the file system level, and then decides what to do with the incoming data based on, say, the file's header, etc., and ultimately back via the OS, with further layers to the DAC per se, which "knows" nothing of the rest, its job is to convert the incoming LPCM audio signal (e.g. in I2S format) to analogue; e.g. whether it got there via optical S/PDIF or USB is immaterial.
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Anyway, the point is that all of these "layers," which could go on ad infinitum, are simply abstracted away.
Yes, another case of using dithering alone, without relation to quantizing.Talking of hard drives, a quick search yields this:
Patent: Hard disk drive head-disk interface dithering. (Assignee: Western Digital.)
Why not? Preserving the maximum amount of information remains a thing, despite your failure to admit "information" is a measurable quantity.I would mostly agree here. The applied math can not be used in this case, because we don't know the application area of the signal.
And the best strategy for quantizing unknown signal is rounding as it provides the best Signal-to-Quantization-Noise Ratio.
Linearization of quantizer by dithering results in increase of quantization error (SQNR). We need some reason for such increase. The reason is in psychoacoustics - increased error is less audible and more pleasant for hearing.You are not making a meaningful measurement UNTIL YOU LINEARIZE THE QUANTIZER and that is DITHER.
Linearization of quantizer by dithering results in increase of quantization error (SQNR). We need some reason for such increase. The reason is in psychoacoustics - increased error is less audible and more pleasant for hearing.
The reason is in psychoacoustics
increased error is less audible and more pleasant for hearing
I would mostly agree here. The applied math can not be used in this case, because we don't know the application area of the signal.
Applying your example to audio signals we could similarly say the following. Operating on the semantic level of audio signal (mixing, applying effects, ...) we can abstract away the engineering level only if corresponding operations on this level do not degrade the signal on the semantic level (properly coded in 32bit arithmetics). In other words, engineering level of audio information can be abstracted away only being fully transparent for semantic level.
You obviously havent heard 8 bit audio with and without dither.
Linearization of quantizer by dithering results in increase of quantization error (SQNR). We need some reason for such increase. The reason is in psychoacoustics - increased error is less audible and more pleasant for hearing.
So, the linearization is required by psychoacoustics, not by math.
This means that for some signals (clean) dithering is required and for others (noisy) is not, which is an indirect indication that this operation is not universal/mathematical. One can object that in this case the dithering happened naturally and exists in the signal anyway.
Linearization of quantizer in audio is required by psychoacoustic properties of hearing.
In this sense the dithering can be considered as simple psychoacoustic trick
When I spent years getting data on molecular vibrations from interferometer signals well below the quantization limit, I had no idea I was using psychoacoustics. I'm glad someone set me straight.
Ditto when pulling data from an accelerometer that is self-dithered by self-noise.
What was this accelerometer used to measure?
The ground.
The applied math can not be used in this case...
...the linearization is required by psychoacoustics, not by math...
...math can not recognize if the signal is noisy or clean. This can be recognized only by Humans. From math point of view these signals are equal.
hat the dithered flac file is larger than the non-dithered flac file is another way that math tells us the dithered file contains more information. No psycho-acoustic interpretation required--just math.
I'll attach the wave files I used. Note the size difference of the zipped files. The non-dithered file is much smaller because it contains less information. The files will unzip/inflate to the same size.