CANONICAL REPRESENTATION OF A CLASS OF LINEAR DISCRETE-TIME TIME-VARIANT SYSTEMS
Date
1985-08
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Journal ISSN
Volume Title
Publisher
ORCID
Type
Degree Level
Masters
Abstract
A particular class of linear discrete-time systems can be characterized by a (square) matrix of system coefficients [H]. The system is time-invariant if [H ] is circulant and time-variant if [In is non-circulant. It is shown that a linear discrete-time time-variant system can be decomposed into a combination of subsystems where each subsystem consists of a linear discrete-time time-invariant system in cascade with a modulator (canonical representation). The canonical representation results from a linear system interpretation of the following matrix decomposition : A PXP matrix [II] (complex in general) can be decomposed as
P-1
[H] = [AT(i)] [H,(1)]
i=0
where [H,(1)] is a circulant matrix and the diagonal matrix[AT(1)] diag {T }, with T(i) denoting the complex conjugate of the i-th column of a PXP Discrete Fourier Transform matrix. The above matrix decomposition can also be interpreted as a (two dimensional) symmetrical component decomposition of [H ]. Since a sampled and quantized image can be represented by a matrix, an application involving image representation in terms of its symmetrical components is presented.
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Degree
Master of Science (M.Sc.)
Department
Electrical Engineering