The theoretical contents of this thesis are studies of overcomplete models. Those are the models of signals, on which is set for their parametrization more variables, than it's necessary and consequently there's computed so-called sparse solution via iteration algorithms. A goal of this analysis is a selection just of the considerable (sparse) parameters. The theory is based on a linear algebra, vector spaces, bases and so-called frames. The task of the individual project of this thesis is a description and simulation of two speech coders: a classical coder based on linear predictive speech coding and a coder, that's making use of overcomplete stochastic ARMA processes models. A part of their realization is to simulate their decoders and a analyze their reconstruction quality. For their realization there is used MATLAB and an overcomplete models' library (toolbox frames)
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