Algebraic Signal Processing Theory: 1-D Nearest Neighbor Models

被引：22

作者：

Sandryhaila, Aliaksei ^{[1
]}

Kovacevic, Jelena ^{[1
,2
]}

Pueschel, Markus ^{[3
]}

机构：

[1] Carnegie Mellon Univ, Dept Elect & Comp Engn, Pittsburgh, PA 15213 USA

[2] Carnegie Mellon Univ, Dept Biomed Engn, Pittsburgh, PA 15213 USA

[3] ETH, Dept Comp Sci, Zurich, Switzerland

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2012年 / 60卷 / 05期

关键词：

Algebra; convolution; filter; Fourier transform; Hermite polynomials; Laguerre polynomials; Legendre polynomials; module; orthogonal polynomials; signal representation; shift; signal model; TUKEY-TYPE ALGORITHMS; POLYNOMIAL-TRANSFORMS; FEATURES;

D O I：

10.1109/TSP.2012.2186133

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials. We demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest neighbor shift introduced in this paper. Using the algebraic signal processing theory, we construct signal models based on this shift and derive their corresponding signal processing concepts, including the proper notions of signal and filter spaces, z-transform, convolution, spectrum, and Fourier transform. The presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials.

引用

页码：2247 / 2259

页数：13

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