Linear and circular digital spectral analysis of serial data

Abstract

Two methods of digital spectral analysis of unevenly sampled data are developed and illustrated here. One method uses a linear function of time (or space), the other uses circular functions. The circular method turns out to be essentially equivalent to a least-squares sine-wave analysis. The linear, anharmonic method uses only the field of real numbers and elementary algebraic operations, and hence it can be made computationally very fast and accurate. Both methods are very general, properly handling all kinds of time series ranging from simple series consisting only of the times of events to complicated series consisting of pulses with long duty cycles. The two methods are here applied to the analysis of annual mean relative sunspot numbers.