Reconstruction of stationary and non-stationary signals by the generalized Prony method

被引：7

作者：

Plonka, Gerlind ^{[1
]}

Stampfer, Kilian ^{[2
]}

Keller, Ingeborg ^{[1
]}

机构：

[1] Gottingen Univ, Inst Numer & Appl Math, Lotzestr 16-18, D-37083 Gottingen, Germany

[2] Gottingen Univ, Inst Math Stochast, Goldschmidtstr 7, D-37077 Gottingen, Germany

来源：

ANALYSIS AND APPLICATIONS | 2019年 / 17卷 / 02期

关键词：

Generalized Prony method; exponential sums; trigonometric sums; modulated Gaussian windows; Gaussian chirps; non-stationary signals; signal reconstruction; empirical mode decomposition; FINITE RATE; DECOMPOSITION; INTERPOLATION; INNOVATION;

D O I：

10.1142/S0219530518500240

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We employ the generalized Prony method in [T. Peter and G. Plonka, A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators, Inverse Problems 29 (2013) 025001] to derive new reconstruction scheme for a variety of sparse signal models using only a small number of signal measurements. By introducing generalized shift operators, we study the recovery of sparse trigonometric and hyperbolic functions as well as sparse expansions into Gaussians chirps and modulated Gaussian windows. Furthermore, we show how to reconstruct sparse polynomial expansions and sparse non-stationary signals with structured phase functions.

引用

页码：179 / 210

页数：32

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