Multi-Phase Locking Value: A Generalized Method for Determining Instantaneous Multi-Frequency Phase Coupling.

BACKGROUND: Many physical, biological and neural systems behave as coupled oscillators, with characteristic phase coupling across different frequencies. Methods such as n : m phase locking value (where two coupling frequencies are linked as: mf 1 = nf 2) and bi-phase locking value have previously been proposed to quantify phase coupling between two resonant frequencies (e.g. f, 2f/3) and across three frequencies (e.g. f 1, f 2, f 1 + f 2), respectively. However, the existing phase coupling metrics have their limitations and limited applications. They cannot be used to detect or quantify phase coupling across multiple frequencies (e.g. f 1, f 2, f 3, f 4, f 1 + f 2 + f 3 - f 4), or coupling that involves non-integer multiples of the frequencies (e.g. f 1, f 2, 2f 1/3 + f 2/3). NEW METHODS: To address the gap, this paper proposes a generalized approach, named multi-phase locking value (M-PLV), for the quantification of various types of instantaneous multi-frequency phase coupling. Different from most instantaneous phase coupling metrics that measure the simultaneous phase coupling, the proposed M-PLV method also allows the detection of delayed phase coupling and the associated time lag between coupled oscillators. RESULTS: The M-PLV has been tested on cases where synthetic coupled signals are generated using white Gaussian signals, and a system comprised of multiple coupled Rössler oscillators, as well as a human subject dataset. Results indicate that the M-PLV can provide a reliable estimation of the time window and frequency combination where the phase coupling is significant, as well as a precise determination of time lag in the case of delayed coupling. This method has the potential to become a powerful new tool for exploring phase coupling in complex nonlinear dynamic systems.

Efficient implementation of LMS adaptive filter-based FECG extraction on an FPGA.

In this Letter, the field programmable gate array (FPGA) implementation of a foetal heart rate (FHR) monitoring system is presented. The system comprises a preprocessing unit to remove various types of noise, followed by a foetal electrocardiogram (FECG) extraction unit and an FHR detection unit. To improve the precision and accuracy of the arithmetic operations, a floating-point unit is developed. A least mean squares algorithm-based adaptive filter (LMS-AF) is used for FECG extraction. Two different architectures, namely series and parallel, are proposed for the LMS-AF, with the series architecture targeting lower utilisation of hardware resources, and the parallel architecture enabling less convergence time and lower power consumption. The results show that it effectively detects the R peaks in the extracted FECG with a sensitivity of 95.74-100% and a specificity of 100%. The parallel architecture shows up to an 85.88% reduction in the convergence time for non-invasive FECG databases while the series architecture shows a 27.41% reduction in the number of flip flops used when compared with the existing FPGA implementations of various FECG extraction methods. It also shows an increase of 2-7.51% in accuracy when compared to previous works.