Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

被引：3

作者：

Ward, John Paul ^{[1
]}

Kirshner, Hagai ^{[1
]}

Unser, Michael ^{[1
]}

机构：

[1] STI, EPFL, CH-1015 Lausanne, Switzerland

来源：

IEEE SIGNAL PROCESSING LETTERS | 2012年 / 19卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Approximation theory; sampling theory; stochastic processes; IDENTIFICATION; SIGNALS; MODEL;

D O I：

10.1109/LSP.2012.2185695

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 consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternative description of poles in the complex plane. We then utilize Kronecker's approximation theorem and prove that the set of non-unique continuous-time AR(2) models has Lebesgue measure zero in this plane. This is a key aspect in current estimation algorithms that use sampled data, as it allows one to remove the sampling rate constraint that is imposed currently.

引用

页码：183 / 186

页数：4

共 16 条

[1]

[Anonymous], 1932, J LONDON MATH SOC

[2]

[Anonymous], 1999, SYSTEM IDENTIFICATIO

[3] Estimation of continuous-time AR process parameters from discrete-time data [J].