## Dither for already recorded 16 bit audio

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Reply #24 –

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* Triangular PDF white noise is the result of adding two independent (i.e. uncorrelated) sources of rectangular PDF white noise. As the number of uncorrelated sources of rectangular white noise you add increases, the resulting probability function of that sum approaches a gaussian bell curve. This is why gaussian PDFs (or the "Normal Distribution") is observed so much in nature at the macroscopic level we normally see, even when the underlying probability distributions at the microscopic level may be very un-gaussian. This is a case of the Central Limit Theorem, and starting with rectangular PDF, one approaches something fairly Gaussian quite quickly. Even the triangular PDF has the beginnings of a crude bell curve shape about its PDF.

May be this article helps: dither basics. It deals with the errors introduced when no dither is applied. Nice to see is that convolution rectangular PDF's will result in a more and more uncorrelated error-signal relationship. At the expense of adding noise power and this sets the limit. In short: one RPDF eliminantes the first moment of the stochast, a TPDF (two RPDF's convoluted) removes the first and second moment (being non-linear distortion and noise modulation respectively) and so on. An infinite number of RPDF's convoluted would be ideal from a statistical moment perspective, but in practise this cannot be realised. 2 or 3 Rectangular PDF's convoluted seems to be sufficient.

Regards,

Jacco