Approximation of a Linear Shift–Variant System by a Set of Linear Shift– Invariant Systems...
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Transcript of 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 SystemsVasile Buzuloiu*, Marius Malciu*†, Sanjit K. Mitra‡
* University “Politehnica” of Bucureşti, România† CERN, Geneva, Switzerland‡ University of California at Santa Barbara, USA
Abstract
We present a method to approximate the impulse response of a LSV (Linear Shift-Variant) system by the impulse responses of a set of LSI (Linear Shift-Invariant) systems which process in parallel on various windowed versions of the input signal
The method is outlined for one-dimensional systems
The extension to the multidimensional case is straightforward
Motivation
The interest for such a subject There are enough examples for which the linearity is
an acceptable hypothesis for the practical range of the variables, but the shift-invariance is not
The LSI property is a very useful one as it allows easy analysis and design of the systems
The approximation is useful for image restoration
Remark
The windows are not LSI blocks Nevertheless this gives a standard
structure for separating the LSI and LSV parts of the system