A nonlinear harmonic analyzer COMPAL.

Abstract

A nonlinear method of least squares has been developed. The combination of the solution of the normal equations, the variational method, and the method of successive approximation, is used to give a compact approximation formula of sequential data. The method is superior to the usual method of nonlinear programming in that not only parameters but the number and form of basic functions are optimized.The method has been realized in COMPAL, the FORTRAN program for nonlinear harmonic analysis. Numerical tests show its merits to be as follows ; 1〕 data are reproduced at any precision one likes as a linear combination of cosine waves with optimal amplitudes, frequencies and phases, 2) a high resolution is assured through a wide frequency range, 3) the variance of estimated frequency is evaluated as well as those for other estimates, 4) waves with different orders of magnitudes are detached, 5) it can handle waves whose wavelength is longer than the data length, 6) it works whether random noise is included in the data or not, 7) trend is determined simultaneously with other parameters, 8) the optimal number of terms of approximation formula is effectively determined. Key Words: method of least squares-nonlinear programming-spectral analysis-multi-periodic phenomena