Fast ESPRIT algorithms based on partial singular value decompositions

Potts, Daniel; Tasche, Manfred

doi:10.1016/j.apnum.2014.10.003

Cited by 29 publications

(16 citation statements)

References 19 publications

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“…In one variable, this problem and its solution date back to Prony (Prony, 1795) in 1795 and since then various numerical methods have been devised to solve the problem, in particular the ESPRIT and MUSIC algorithms (Roy and Kailath, 1989;Schmidt, 1986) from multi source radar detection with extensions to higher dimensions on grids in (Rouquette and Najim, 2001;Yilmazer et al, 2006). One should also consider (Potts and Tasche, 2015) for recent improvements and (Plonka and Tasche, 2014) for a survey on Prony's method and its extensions and generalizations. The matrix pencil approach for the Hankel matrices has also been considered in (Hua and Sarkar, 1990;Hua, 1992) in one and two variables.…”

Section: Introductionmentioning

confidence: 99%

Prony's method in several variables: Symbolic solutions by universal interpolation

Sauer

2018

Journal of Symbolic Computation

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Section: Introductionmentioning

confidence: 99%

Prony's method in several variables: Symbolic solutions by universal interpolation

Sauer

2018

Journal of Symbolic Computation

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“…In the polynomial method, small variations in the coefficients of equation ( 2 ) due to signal noise can result in large variations in its zeros and, consequently, the frequencies of the approximation will vary greatly. Parametric spectral estimation techniques, such as MUSIC (MUltiple SIgnal Classification) [ 50 ], ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) [ 51 ] or fast ESPRIT [ 52 ] offer an alternative that in many cases make it possible to obtain more robust solutions. [ 53 ] presents an algorithm for the factorization of a matrix pencil based on QR decomposition of a rectangular Hankel matrix, which simplifies the ESPRIT method.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2018

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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.

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“…In this respect it can be considered an extension of the well-known MUSIC [40] and ESPRIT [34] methods, where zero eigenvectors of a symmetric and positive semidefinite measurement covariance matrix are determined and set an eigenvalue problem. A more sophisticated variant of ESPRIT can be found in [32]. As pointed out in [31], the Frobenius companion matrix of the Prony polynomial interacts nicely with the Hankel matrix of the samples which can be used to define a generalized eigenvalue problem for matrix pencils, see [17].…”

Section: Comparison To Existing Methodsmentioning

confidence: 99%