## 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 $$f(z) = \sum_{\lambda\in\Lambda} \kappa_{f}(\lambda)\frac{e^{\lambda z}}{L^{\prime}(\lambda)}, \quad z\in D$$ on a convex polygon $D$ as a generalization of Fourier series. Here $L$ denotes a quasipolynomial whose set of zeros $\Lambda$ generates a Riesz basis ${\cal E}(\Lambda) := \left\{\frac{e^{\lambda z}}{L^{\prime}(\lambda)}\right\}_{\lambda\in\Lambda}$ 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 ${\cal E}(\Lambda)$.

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### Key words

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

### AMS subject classifications

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

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