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Пишет Best Linear Unbiased Predictor (![[info]](http://lj.rossia.org/img/userinfo.gif){kind=small} measure_01)@ 2010-10-11 14:04:00 |
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Algebraic Signal processing Theory
When I began studying DSP, the first question that came to my mind was: "how to formalize signals in terms of algebraic structures?".
Later I've found a paper devoted to algebraic signal processing. Here the main concepts of SP theory are written in the language of modern algebra: filters are an algebra (usually commutative), signals are a module over the algebra of filters, Fourier transform is a homomorphism from A-module of signals to itself, z-transform is a functor from the category of A-modules to the category of polynomial algebras, etc.
There is also a very nice table that assigns an associated A-module and filter algebra to a system of each type (in engineering sense). :)
When I began studying DSP, the first question that came to my mind was: "how to formalize signals in terms of algebraic structures?".
Later I've found a paper devoted to algebraic signal processing. Here the main concepts of SP theory are written in the language of modern algebra: filters are an algebra (usually commutative), signals are a module over the algebra of filters, Fourier transform is a homomorphism from A-module of signals to itself, z-transform is a functor from the category of A-modules to the category of polynomial algebras, etc.
There is also a very nice table that assigns an associated A-module and filter algebra to a system of each type (in engineering sense). :)
