On fast RMS estimation for digital data

Abstract

This paper presents a new algorithm for fast evaluating the accuracy of root mean square (RMS) estimation for digital data. The algorithm is developed to accelerate the determination of estimation errors. The new algorithm is based on a non-iterative estimator of the RMS parameter and is equivalent to the classical PQN (CPQN) algorithm, which uses an iterative RMS estimator calculated from samples of a harmonic signal occurring in the presence of a constant component (offset), Gaussian noise, and pseudo-quantization noise (PQN) as proposed by Widrow and Kollár. The developed algorithm was called FPQN (fast PQN) and compared with the CPQN algorithm. The classical quantization noise (CQN) algorithm, which is based on an iterative RMS estimator calculated from quantized signal samples, was also used in the comparative studies. The algorithms were compared based on the mean squared errors of the estimators returned by the algorithms. Additionally, the execution times of the algorithms were measured for comparison. The results show that errors of the new algorithm are comparable to those of the CPQN and CQN algorithms. Simultaneously, the new algorithm is several times faster, and its advantage is enhanced as the number of samples in the measurement window increases. For a window containing 200–1000 samples, the developed algorithm is 18–94 times faster than CPQN and 24–120 times faster than CQN.