Determination of fundamental frequency of a physical oscillator by the period fitting method

A period fitting method, which is a variant of the classical least-square f itting method, is proposed to determine the fundamental frequency of a phys ical oscillator. The root mean square deviation used as the criterion in th is method is a single-parameter function of the fundamental frequency of th e oscillator, so it makes the fitting process optimize the period fit at th e expense of a lesser evaluation of the other parameters such as the amplit ude and the phase. Theoretical analysis shows that this method is intrinsic ally independent of the disturbances of the high order harmonic frequencies oscillation, and the computer simulation experiments show that it is effec tive to overcome the disturbances of the finite quality factor and the mono tonic drift of an oscillator system, as well as the white noise, and this m ethod can determine the fundamental frequency or period of a physical oscil lator with a relative precision of 10(-7) orders. (C) 1999 American Institu te of Physics. [S0034-6748(99)02511-3].