Potts, Daniel ; Tasche, Manfred : An inverse problem of digital signal processing

Author(s):

Potts, Daniel
Tasche, Manfred

Title:

An inverse problem of digital signal processing

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 9, 2009

Mathematics Subject Classification:

42C15			[ Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions ]
65T40			[ Trigonometric approximation and interpolation ]
65T50			[ Discrete and fast Fourier transforms ]
65F15			[ Eigenvalues, eigenvectors ]
65F20			[ Overdetermined systems, pseudoinverses ]
94A12			[ Signal theory ]

Abstract:

An important problem of digital signal processing is the so-called frequency analysis problem: Let $f$ be an anharmonic Fourier sum. Determine the different frequencies, the coefficients, and the number of frequencies 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 which is based on \cite{BeMo02, BeMo05}. In contrast to \cite{BeMo02, BeMo05}, we apply matrix perturbation theory such that we can describe the properties and the numerical behavior of the approximate Prony method in detail. Numerical experiments show the performance of our method.

Keywords:

frequency analysis problem, nonequispaced fast Fourier transform, digital signal processing, anharmonic Fourier sum, approximate Prony method, matrix perturbation theory, perturbed Hankel matrix, Vandermonde-type matrix

Language:

English

Publication time:

4 / 2009