Coding Prony's method in MATLAB and applying it to biomedical signal filtering

Background:The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony's method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results:The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions:This paper reviews Prony's method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above.Universidad de AlcaláSecretaría de Estado de Investigación, Desarrollo e Innovació

Comparison of modelled pursuits with ESPRIT and the matrix pencil method in the modelling of medical percussion signals

The objective of this paper is to compare Modelled Pursuits (MoP), a recently developed iterative signal decomposition method, with more established matrix based subspace methods used to aid or automate medical percussion diagnoses. Medical percussion is a technique used by clinicians to aid the diagnosis of pulmonary disease. It requires considerable expertise, so it is desirable to automate this process where possible. Previous work has examined the application of modal decomposition techniques, since medical percussion signals (MPS) can be intuitively characterised as combinations of exponentially decaying sinusoidal (EDS) vibrations. Best results have typically been reported with matrix based subspace methods such as Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) and the Matrix Pencil Method (MPM). Since ESPRIT and MPM are computationally expensive, this paper investigates whether an iterative method such as MoP can produce similar results with less computation and/or memory overheads. Using randomly generated synthetic signals designed to replicate typical ‘tympanic’ and ‘resonant’ percussion signals, we compared each method: MoP, ESPRIT, and MPM, for accuracy, speed and memory usage. We find that for low Signal to Noise Ratios (SNRs) MoP gives less accuracy than both ESPRIT and MPM, however for high SNRs (as would be typically encountered in a clinical setting) it is more accurate than MPM but less accurate than ESPRIT. We conclude that in embedded clinical applications where both operations-per-second and memory-usage are a factor, MoP is less computationally intensive than ESPRIT and thus is worth considering for use in those contexts

Automated Classification of Medical Percussion Signals for the Diagnosis of Pulmonary Injuries

Used for centuries in the clinical practice, audible percussion is a method of eliciting sounds by areas of the human body either by finger tips or by a percussion hammer. Despite its advantages, pulmonary diagnostics by percussion is still highly subjective, depends on the physician\u27s skills, and requires quiet surroundings. Automation of this well-established technique could help amplify its existing merits while removing the above drawbacks. In this study, an attempt is made to automatically decompose clinical percussion signals into a sum of Exponentially Damped Sinusoids (EDS) using Matrix Pencil Method, which in this case form a more natural basis than Fourier harmonics and thus allow for a more robust representation of the signal in the parametric space. It is found that some EDS represent transient oscillation modes of the thorax/abdomen excited by the percussion event, while others are associated with the noise. It is demonstrated that relatively few EDS are usually enough to accurately reconstruct the original signal. It is shown that combining the frequency and damping parameters of these most significant EDS allows for efficient classification of percussion signals into the two main types historically known as resonant and tympanic . This classification ability can provide a basis for the automated objective diagnostics of various pulmonary pathologies including pneumothorax

Inter-Microgrid Operation: Power Sharing, Frequency Restoration, Seamless Reconnection and Stability Analysis

Electrification in the rural areas sometimes become very challenging due to area accessibility and economic concern. Standalone Microgrids (MGs) play a very crucial role in these kinds of a rural area where a large power grid is not available. The intermittent nature of distributed energy sources and the load uncertainties can create a power mismatch and can lead to frequency and voltage drop in rural isolated community MG. In order to avoid this, various intelligent load shedding techniques, installation of micro storage systems and coupling of neighbouring MGs can be adopted. Among these, the coupling of neighbouring MGs is the most feasible in the rural area where large grid power is not available. The interconnection of neighbouring MGs has raised concerns about the safety of operation, protection of critical infrastructure, the efficiency of power-sharing and most importantly, stable mode of operation. Many advanced control techniques have been proposed to enhance the load sharing and stability of the microgrid. Droop control is the most commonly used control technique for parallel operation of converters in order to share the load among the MGs. But most of them are in the presence of large grid power, where system voltage and frequency are controlled by the stiff grid. In a rural area, where grid power is not available, the frequency and voltage control become a fundamental issue to be addressed. Moreover, for accurate load sharing a high value of droop gain should be chosen as the R/X ratio of the rural network is very high, which makes the system unstable. Therefore, the choice of droop gains is often a trade-off between power-sharing and stability. In the context, the main focus of this PhD thesis is the fundamental investigations into control techniques of inverter-based standalone neighbouring microgrids for available power sharing. It aims to develop new and improved control techniques to enhance performance and power-sharing reliability of remote standalone Microgrids. In this thesis, a power management-based droop control is proposed for accurate power sharing according to the power availability in a particular MG. Inverters can have different power setpoints during the grid-connected mode, but in the standalone mode, they all need their power setpoints to be adjusted according to their power ratings. On the basis of this, a power management-based droop control strategy is developed to achieve the power-sharing among the neighbouring microgrids. The proposed method helps the MG inverters to share the power according to its ratings and availability, which does not restrict the inverters for equal power-sharing. The paralleled inverters in coupled MGs need to work in both interconnected mode and standalone mode and should be able to transfer between modes seamlessly. An enhanced droop control is proposed to maintain the frequency and voltage of the MGs to their nominal value, which also helps the neighbouring MGs for seamless (de)coupling. This thesis also presents a mathematical model of the interconnected neighbouring microgrid for stability and robustness analysis. Finally, a laboratory prototype model of two MGs is developed to test the effectiveness of the proposed control strategies