Optimised Spectral Density Shaping of Quantisation Error Using Adaptive 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 using a joint specification of the probability density function (PDF) and the PSD by way of stochastic minimisation (SM). The output of the quantiser can be made linear and continuous in the mean and the variance of the error can be made independent of the quantiser input by using a dither with a triangular PDF. However, shaping the error PSD to a desired form for reconstruction at the quantiser output remains input dependent. An adaptive dithering approach is implemented to address this dependency. By exploiting symmetry properties of uniform quantisation, it is possible to use SM to generate a limited number of dither sequences and reuse them to shape the total error PSD for arbitrary inputs. The approach is implemented using a look-up table (LUT). When optimised for reconstruction filtering, simulation results demonstrate an improved PSD shaping performance over the state-of-the-art feed-forward method of over two orders of magnitude within a given bandwidth.