Statistical properties of quantisation noise in analogue‐to‐digital converter with oversampling and decimation

Abstract

This study presents the analysis of statistical parameters of the output quantisation noise amplitude distribution in the analogue-to-digital converter (ADC) with oversampling and decimation. Hypothesis was tested that quantisation noise amplitudes on the output of the system have a Gaussian distribution. To test this hypothesis, Chi-squared statistical test was performed with parameter estimation based on grouped data. Simulation models were made for two types of ADCs: classical b-bit and sigma–delta. Various realisations of decimation filters were used as well as various values of the decimation factor. Based on the number of cases in which the hypothesis was rejected, the significance of the test was determined, i.e. the deviation from the ideal Gaussian distribution was quantified. Results of this research can prove to be useful in system design process, where accurate knowledge of the quantisation noise statistical model parameters is required. This study presents general procedure for analysing the amplitude distribution of the quantisation noise, which can easily be implemented on other modified models of the ADC with oversampling.