Dither—my explanation of how it keeps details below quantization level, Was: "Dither" (TOS #6) Options

[KMD]

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.

[benski]

I remember the first lab in University Physics class. We were given a rectangular block and asked to determine its length given only a ruler with centimeter markings.

For the sake of discussion, let's assume the object is 57mm long. If you measure from the start of the ruler, you will get 50mm (5 cm) every time, as the ruler is only that precise. If you measure from the opposite end of the ruler, you will get 60mm every time. However, if you randomly place the ruler against the block, you will sometimes measure 50mm and sometimes measure 60mm. If you repeat with enough trials and average the results, you will converge at the appropriate value: 57mm.

This is an almost perfect analogy for how dither works. By adding in noise, you are essentially "randomly placing the ruler".

If you were to imagine a DC signal at 0.6 that is being decimated to integer values. By randomly adding noise, each sample value will be either 1 or 0, and their appearance should occur in a 6:4 ratio, and the RMS energy of the decimated, dithered signal will be 0.6 - the same as the original signal.

Error shaping works by "feeding forward" the prior error to increase the likelihood that the next value will offset the previous error.

This post has been edited by benski: Mar 21 2012, 21:44