Matrix analysis
Digital spectral analysis: with applications
Digital spectral analysis: with applications
ESPRIT-estimation of signal parameters via rotational invariance techniques
Signal processing part II
Application of Szego¨ polynomials to frequency analysis
SIAM Journal on Mathematical Analysis - Special issue: the articles in this issue are dedicated to Richard Askey and Frank Olver
A Stable Numerical Method for Inverting Shape from Moments
SIAM Journal on Scientific Computing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Stability Results for Scattered Data Interpolation by Trigonometric Polynomials
SIAM Journal on Scientific Computing
Numerical stability of nonequispaced fast Fourier transforms
Journal of Computational and Applied Mathematics
Fast recursive low-rank linear prediction frequency estimationalgorithms
IEEE Transactions on Signal Processing
Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix
IEEE Transactions on Signal Processing
Total least squares phased averaging and 3-D ESPRIT for jointazimuth-elevation-carrier estimation
IEEE Transactions on Signal Processing
Nonlinear Approximation by Sums of Exponentials and Translates
SIAM Journal on Scientific Computing
Representation of sparse Legendre expansions
Journal of Symbolic Computation
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The recovery of signal parameters from noisy sampled data is a fundamental problem in digital signal processing. In this paper, we consider the following spectral analysis problem: Let f be a real-valued sum of complex exponentials. Determine all parameters of f, i.e., all different frequencies, all coefficients, and the number of exponentials from finitely many equispaced sampled data of f. This is a nonlinear inverse problem. In this paper, we present new results on an approximate Prony method (APM) which is based on [1]. In contrast to [1], we apply matrix perturbation theory such that we can describe the properties and the numerical behavior of the APM in detail. The number of sampled data acts as regularization parameter. The first part of APM estimates the frequencies and the second part solves an overdetermined linear Vandermonde-type system in a stable way. We compare the first part of APM also with the known ESPRIT method. The second part is related to the nonequispaced fast Fourier transform (NFFT). Numerical experiments show the performance of our method.