Coding Prony's method in MATLAB and applying it to biomedical signal filtering
…, E López Guillén, JM Rodríguez Ascariz… - BMC …, 2018 - Springer
A Fernández Rodríguez, L de Santiago Rodrigo, E López Guillén, JM Rodríguez Ascariz…
BMC bioinformatics, 2018•SpringerBackground 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 (eg 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 …
combination of damped exponential functions. The approximation parameters, based on
equally spaced samples, can be obtained using Prony's method and its variants (eg 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 …
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.
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