Approximation of a linear shift variant system by a set of linear shift invariant systems
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Approximation of a Linear Shift–Variant System by a Set of Linear Shift–Invariant Systems. Vasile Buzuloiu * , Marius Malciu * †, Sanjit K. Mitra‡ * University “Politehnica” of Buc u re ş t i , Rom â nia † CERN, Geneva , Switzerland ‡ University of California at Santa Barbara , USA. Outline.

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Approximation of a linear shift variant system by a set of linear shift invariant systems

Approximation of a Linear Shift–Variant System bya Set of Linear Shift–Invariant Systems

Vasile Buzuloiu*, Marius Malciu*†, Sanjit K. Mitra‡

* University “Politehnica” of Bucureşti, România

† CERN, Geneva, Switzerland

‡ University of California at Santa Barbara, USA


Outline
Outline

  • Introduction

  • Our method

  • Application to one-dimensional systems


Abstract
Abstract

  • We present a method to approximate theimpulse response of a LSV (Linear Shift-Variant) system by the impulseresponses of a set of LSI (Linear Shift-Invariant) systems which processin parallel on various windowed versions of the input signal

  • Themethod is outlined for one-dimensional systems

  • The extensionto the multidimensional case is straightforward


Motivation
Motivation

  • The interest for such a subject

    • There are enough examples for which the linearity is an acceptable hypothesis for thepractical range of the variables, but the shift-invariance is not

    • The LSI property is a very useful one as it allows easyanalysis and design of the systems

    • The approximation is useful for image restoration




Decomposing h t in bricks
Decomposing h(t,τ) in bricks


Decomposing h t in bricks 2
Decomposing h(t,τ) in bricks (2)






Remark
Remark

  • The windows are not LSI blocks

  • Nevertheless this gives a standard structure for separating the LSI and LSV parts of the system



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