Spectral Density Shaping of Quantisation Error Using Dithering

Abstract

A method for shaping the power spectral density (PSD) of the total error due to uniform quantisation is proposed. It utilises non subtractive dithering, generated with a joint specification of the probability density function (PDF) and the PSD. If the dither PDF has certain properties, the expected value of the quantiser output can be linearised and the variance of the error (the error power) can be made independent of the quantiser input. It is demonstrated that making the error power independent of the input enables shaping the error PSD as a separate problem. The method relies on the use of a linear noise colouring filter and a static non-linear transform, which imposes some restrictions on the specification of the error PSD. However, it is possible to synthesise a range of filters that can be used to shape the PSD of the error. Simulations are provided to verify and illustrate the operation of the method.