Abstract
BackgroundThe 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).ResultsThe 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).ConclusionsThis 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.
Highlights
The response of many biomedical systems can be modelled using a linear combination of damped exponential functions
This paper presents a tutorial on implementation in MATLAB of two families of Prony methods: the polynomial method and the matrix pencil method
The methods described are applied in two situations: a) approximation of synthetic signals and b) filtering of multifocal visual-evoked potential (mfVEP) signals
Summary
The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. 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 conventional or polynomial Prony method consists of setting out an autoregressive model of order p that assumes that the value of sampled data x[n] depends linearly on the preceding p values in x. Solving this linear system of equations obtains the coefficients of the characteristic or Prony polynomial φ(z). The roots of this polynomial yield two of the parameters of the solution (damping factors and frequency) and provide a second system of Fernández Rodríguez et al BMC Bioinformatics (2018) 19:451 equations to calculate the amplitude and phase of the p functions
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