........................................................................................................................ iv LIST OF TABLES ............................................................................................................... ix LISTOF FIGURES ............................................................................................................... x CHAPTER ONE: I...

A modification of the classical technique of Prony for fitting sums of exponential functions to data is considered. The method maximizes the likelihood for the problem (unlike the usual implementation of Prony’s method, which is not even consistent for transient signals), proves to be remarkably effective in practice, and is supported by an asymptotic stability result. Novel features include a ...

Prony 's method is employed in spectral domain estimation to model epilepsy seizure from human's electroencephalograph (EEG).This method assumes that the original signal is a sum of damped complex exponential sinusoids. The method has the best frequency resolution compared to Auto Regression (AR) parametric methods. Modeling of the EEG Epilepsy signal is based on the poles of the signal. Comput...

A new fast and accurate algorithm for tracking singular values, singular vectors and the dimension of the signal subspace through an overlapping sequence of data matrices is presented. The accuracy of the algorithm approaches that of the Prony-Lanczos (PL) method [1] with speed and accuracy superior to both the PAST and PASTd algorithms [2] for moderate to large size problems. The algorithm is ...

Abstract — Modern frequency power converters generate a wide spectrum of harmonics components. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. A novel approach to harmonic and interharmonic analysis, based on...

This paper presents a methodology allowing to estimate the parameters of two-dimensional damped/undamped sinusoids from high complexity noisy signals, which is the case in 2-D nuclear magnetic resonance spectroscopy. The proposed approach performs an adaptive subband decomposition combined with a classical frequency estimator based on the Prony model. At each node resulting from the decompositi...

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...

Impact injuries are commonplace in sport and often lead to performance detriment and debilitation. Personal Protective Equipment (PPE) is prescribed as a mandatory requirement in most sports where these impacts are likely to occur, though the methods of governance and evaluation criteria often do not accurately represent sports specific injury scenarios. One of the key shortcomings of such safe...