Volume 14, pp. 45-55, 2002.

An algorithm for nonharmonic signal analysis using Dirichlet series on convex polygons

Brigitte Forster

Abstract

This article presents a new algorithm for nonharmonic signal analysis using Dirichlet series $$f(z)=\sum _{\lambda \in \mathrm{\Lambda }}{\kappa }_f(\lambda )\frac{e^{\lambda z}}{L^{\prime }(\lambda )},z\in D$$ on a convex polygon $D$ as a generalization of Fourier series. Here $L$ denotes a quasipolynomial whose set of zeros $\mathrm{\Lambda }$ generates a Riesz basis $\mathcal{E}(\mathrm{\Lambda }):={\left\{\frac{e^{\lambda z}}{L^{\prime }(\lambda )}\right\}}_{\lambda \in \mathrm{\Lambda }}$ of the Smirnov space $E^2(D)$. The algorithm is based on a simple form of $L$ and on numerical properties of the dual basis of $\mathcal{E}(\mathrm{\Lambda })$.

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Key words

nonharmonic Fourier series, Dirichlet series, signal analysis, time series analysis.

AMS subject classifications

(2000) 42C15, 30B50, 37M10.