Application of the Quotient-Difference Algorithm for Measurement Tasks

An approximation of noisy measurement signals by exponential sums is considered, and the advantages of this method are shown. Methods for estimating parameters of exponential components using parametric methods based on autoregressive models are well established, but time-consuming. Calculation of component parameters for the approximating aggregate is compared using Prony's least squares method, and the quotient-difference (QD) algorithm of Rutishauser. The QD algorithm is based on the application of continued fractions to classical identification problems. The algorithm to find the roots of a polynomial (or the poles of a transfer function) was described by Rutishauser in the late 1950s. However, it was not widely used and confirmed by practical calculations. The authors have proposed and have studied in detail a modified QD algorithm, which adapts to the signal with the given measurement error. It is shown that the use of QD decomposition in combination with the Prony model allows us to solve the problem of signal approximation by exponential functions, parametric analysis (calculating the frequencies and attenuations of components, their amplitudes and phases), spectral analysis based on z-transformation of signal samples, determination of eigenvalues and eigenvectors based on one algorithm, and at the same time significantly reduce the amount of computational work. The possibility of using the Rutishauser algorithm in combination with a preliminary decomposition of the data sequence into elementary oscillatory components is described.