Data-driven optimal filtering for phase and frequency of noisy oscillations: Application to vortex flow metering

Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jan;69(1 Pt 2):016216. doi: 10.1103/PhysRevE.69.016216. Epub 2004 Jan 30.

Abstract

A method for measuring the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flow meters. A measure for the strength of mode locking is proposed.