To help with the understanding of dither, I am posting an explanation, of how signal details smaller than the quantization level are retained, after quantization, when Dither Noise is added to the source material. A small signal detail with height less than the quantization level, and centred half way between two quantization steps, is too small to cross a quantization step. It is lost when the waveform is quantized. With a Dither Noise waveform added, the height of the two waveforms summed is occasionally greater than the quantization level. At these occasional points the waveform crosses a quantization step. So now when this waveform is quantized, although the result is noisy, the shape of the original signal detail is retained. Discussion invited.
You might add that even when that small signal DOES cross quantization steps, it will be highly distorted, e.g. converted into a square wave. Dither will then reduce the distortion.
I highly recommend the first few sections of this thesis for a careful technical explanation of how dither works and why it's important. It starts with the sampling theorem, shows how quantization breaks it, then shows how dither (of the right kind) fixes the breakage. It's well worth the read, even though the latter parts are dealing with image processing rather than audio.
After a quick review I really must question the emphasis that is placed on how dither affects the visual appearance of waveforms. This is clearly not in line with one of the most important tenets of our forum
Dither is random or semi-random noise added to a signal in order to mask quantization noise and/or extend dynamic range. The simplest dither is quiet white noise, but more complicated forms of dither are possible using [[noise shaping]], and they can even be completely inaudible.
Dither is random noise added to a signal in order to increase the degree to which the quantization and sampling process accurately reproduces the image of the input signal. The simplest dither is quiet white noise, but more complicated forms of dither are possible using [[noise shaping]].
Going from 24-bit to 16-bit, the quantization error is very small and the distortion/noise is extremely unlikely to be heard in any real music. Since quantization error isn’t audible in any real music at useable listening levels, whether dither must be used is more a matter of doctrine than functionality.
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