A black box method for solving the complex exponentials approximation problem

Authors:
Piero Barone
Affiliations:
Istituto per le Applicazioni del Calcolo "M. Picone", C.N.R., via dei Taurini 19, 00185 Rome, Italy
Venue:
Digital Signal Processing
Year:
2013

Citing 13
Cited 0

Matrix analysis

Matrix analysis
Some applications of the rank revealing QR factorization

SIAM Journal on Scientific and Statistical Computing
Application of the Pade´ method to solving the noisy trigonometric moment problem: some initial results

SIAM Journal on Applied Mathematics
A Stable Numerical Method for Inverting Shape from Moments

SIAM Journal on Scientific Computing
Reconstruction of a piecewise constant function from noisy Fourier coefficients by Padé method

SIAM Journal on Applied Mathematics
A new transform for solving the noisy complex exponentials approximation problem

Journal of Approximation Theory
On the distribution of poles of Padé approximants to the Z-transform of complex Gaussian white noise

Journal of Approximation Theory
Estimation of a new stochastic transform for solving the complex exponentials approximation problem: Computational aspects and applications

Digital Signal Processing
On SVD for estimating generalized eigenvalues of singular matrixpencil in noise

IEEE Transactions on Signal Processing
Some properties of the asymptotic location of poles of Padeapproximants to noisy rational functions, relevant for modal analysis

IEEE Transactions on Signal Processing
Shape from moments - an estimation theory perspective

IEEE Transactions on Signal Processing
On the condensed density of the generalized eigenvalues of pencils of Gaussian random matrices and applications

Journal of Multivariate Analysis
A Diffusion Equation for the Density of the Ratio of Two Jointly Distributed Gaussian Variables and the Exponential Analysis Problem

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

A common problem, arising in many different applied contexts, consists in estimating the number of exponentially damped sinusoids whose weighted sum best fits a finite set of noisy data and in estimating their parameters. Many different methods exist to this purpose. The best of them are based on approximate Maximum Likelihood estimators, assuming to know the number of damped sinusoids, which can then be estimated by an order selection procedure. As the problem can be severely ill posed, a stochastic perturbation method is proposed which provides better results than Maximum Likelihood based methods when the signal-to-noise ratio is low. The method depends on some hyperparameters which turn out to be essentially independent of the application. Therefore they can be fixed once and for all, giving rise to a black box method.