A Frequency Measure Robust to Linear Filtering

It is noted that the determination of an oscillation frequency by used of the power spectrum of measured time series is susceptible to filtering of the signal. Similarly, frequency measurements made by period counting can yield different results depending on how the signal is filtered for noise reduction. In an attempt to eliminate these ambiguities, a new measure of frequency, based on an approximate reconstruction of the phase-space trajectory of the oscillator from the signal, is introduced. This measure is shown to be invariant under linear filtering. For this reason, it is also inaccessible by spectral methods. The effect of filtering on frequency for weakly nonlinear, noisy oscillators, to which this definition applies only imperfectly, is quantified. This work provides the theoretical basis for frequency measurements employing MIRVA filtering [A. G. Rossberg et al., Phys. Rev. E 69 (2004), 016216].