<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.</p></abstract>

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

Construction of Sampling and Interpolating Sequences for Multi-Band Signals. The Two-Band Case

Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA

Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne Victoria 3010, Australia

International Journal of Applied Mathematics and Computer Science

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of...

Construction of Sampling and Interpolating Sequences for Multi-Band Signals. The Two-Band Case

Published Online: Jul 17, 2007

Page range: 143 - 156

DOI: https://doi.org/10.2478/v10006-007-0013-4

Keywords
sampling and interpolation, multi-band signals, Riesz bases, families of exponentials, Wiener-Hopf equations, control, observation

This content is open access.

Construction of Sampling and Interpolating Sequences for Multi-Band Signals. The Two-Band Case

Published Online: Jul 17, 2007

Page range: 143 - 156

DOI: https://doi.org/10.2478/v10006-007-0013-4

Keywordssampling and interpolation, multi-band signals, Riesz bases, families of exponentials, Wiener-Hopf equations, control, observation

This content is open access.

Keywords
sampling and interpolation, multi-band signals, Riesz bases, families of exponentials, Wiener-Hopf equations, control, observation