Least-squares fitting algorithms applied to periodic signals

Abstract

A new generation of multipurpose measurement equipment is transforming the role of computers in instrumentation. The new features involve mixed devices, as analog-to-digital and digital-to-analog converters, and digital signal processing techniques, able to substitute typical discrete instruments like multimeters, analyzers, etc. Signal-processing applications frequently use least-squares sine-fitting algorithms. Periodic signals may be interpreted as a sum of sine waves with multiple frequencies, the Fourier series. This paper proposes a new algorithm which is able to fit a multi-harmonic acquired signal determining the amplitude and phase of all harmonics. Simulation and experimental results are presented.