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

Abstract

A new method for extracting 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 (MIRVA) 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 flowmeters. A novel measure for the strength of mode locking is proposed.

Towards a proper estimation of phase synchronization from time series

“…A detailed description and discussion of such algorithms can be found in Boashash (1992); Carmona et al (1997Carmona et al ( , 1999; Delprat et al (1992); Le Van Quyen et al (2001); Oliveira and Barroso (1999) and Wei and Bovik (1998). Adaptive or data-driven methods (Huang et al, 1998;Rossberg et al, 2004) could also be an alternative for the analysis of multicomponent signals.…”

A Frequency Measure Robust to Linear Filtering

“…A projection matrix P ( Fig. 1(b)) can be found 22) such that the projection of the 20D embedding of {y t } into 2D yields a trajectory with the nice circular structure and a "hole" in the center displayed in Fig. 1(c).…”

“…A practical method for constructing suitable filters {f k } for a given time series is described in Ref. 22). Such filters, called MIRVA filters there, are optimized to yield a circular structure of the 2D projection, like that seen in Fig.…”

Phase Synchronization from Noisy Univariate Signals

“…In a first experiment, the peak-to-peak flow modulation was ≈ 10% of the average flow rate, and the frequency of the flow pulsation f puls was varied. Due to the symmetry of the setup [18], the strongest phase locking occurs at a frequency ratio of f puls : f vort = 2 : 1. In Fig.…”

“…gives a consistent way to define the phase φ(t) [3,18]. By extracting the phase φ(t), the higher dimensional dynamics of an oscillating system is projected to one dimension.…”