Application of Random Functions to Assess the Influence of Quantization Error on the Signal RMS

Abstract

In modern digital measurement devices to obtain samples in the signal measurement channel, analog-to-digital converters (ADCs) are applied. Real ADCs have finite resolution, which results in time domain to the quantization error effect (so called quantization noise). Regardless of the applied measurement method, the quantization noise results to measurement error of RMS, active power, complex spectrum and other. A research of influence on the ADC parameters (resolution, sampling frequency, input range, ADC architecture type) to the RMS measurement error is carried out. It is established that the most important ADC parameters are resolution and sampling frequency. The proposed RMS error estimating method is based on the application of a parabolic interpolation polynomial function (by the sampling frequency as a parameter). The interpolation polynomial coefficients are determined as a result of simulation modeling which is performed in Matlab 7. Random functions were applied to simulate the quantization noise. Analytical expressions are obtained that allows to estimate the RMS measurement error from the signal parameters and ADC parameters by using the proposed error estimation method. The simulation results show that the proposed method of the error calculation allows at least to reduce the RMS error estimate (in comparison with “worst case” method) at least to 30 %. The proposed approach for the error estimation can be used for sinusoidal signals or polyharmonic signals the shape of which is close to sinusoidal. The application of the proposed approach can be extended to the problem of active power and complex spectrum measurement.