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
