Discrete-Time Multi-Scale Systems

Daniel Alpay; Mamadou Mboup

doi:10.1007/s00020-010-1785-8

Discrete-Time Multi-Scale Systems

Daniel Alpay, Mamadou Mboup

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

Original language	English
Pages (from-to)	163-191
Number of pages	29
Journal	Integral Equations and Operator Theory
Volume	68
Issue number	2
DOIs	https://doi.org/10.1007/s00020-010-1785-8
State	Published - 22 Mar 2010

Keywords

Discrete-scale transformation
linear systems
reproducing kernels
scale invariance
self-similarity

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title = "Discrete-Time Multi-Scale Systems",

abstract = "We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.",

keywords = "Discrete-scale transformation, linear systems, reproducing kernels, scale invariance, self-similarity",

author = "Daniel Alpay and Mamadou Mboup",

note = "Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. This research is part of the European Science Foundation Networking Program HCAA, and was supported in part by the Israel Science Foundation grant 1023/07.",

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AU - Alpay, Daniel

AU - Mboup, Mamadou

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PY - 2010/3/22

Y1 - 2010/3/22

N2 - We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

AB - We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

KW - Discrete-scale transformation

KW - linear systems

KW - reproducing kernels

KW - scale invariance

KW - self-similarity

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EP - 191

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -

Discrete-Time Multi-Scale Systems

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Keywords

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