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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 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

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  1. 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

  2. Outline • Introduction • Our method • Application to one-dimensional systems

  3. 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

  4. 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

  5. Characterization of LSI systems

  6. Characterization of LSV systems

  7. Decomposing h(t,τ) in bricks

  8. Decomposing h(t,τ) in bricks (2)

  9. A 1-D example

  10. How we choose

  11. Consequence

  12. Equivalent block diagram

  13. Remark • The windows are not LSI blocks • Nevertheless this gives a standard structure for separating the LSI and LSV parts of the system

  14. The N-dimensional case

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