WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 10, 2014
Linear Filtering and Modelling based on Gram-Schmidt Orthogonalization Concept
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Abstract: In this work, the approach we suggest for the linear filtering consists in considering any linear filter as a geometric hyper plane space to which the output signal vector belongs. Any signal orthogonal component to this space vanishes. So removing a non desired component from a signal is to look for a flat space to which this component is orthogonal; in other words, this non desired component will not be observed by orthogonal projection in this geometric space or it does not belong to it and hence, it is eliminated according to Gram-Schmidt orthogonalization concept. To clarify this point view, we compare this geometric filtering procedure to that of an ideal low pass filter in Fourier space and show that it is simple, more efficient and general than the traditional filtering. As an application, we extend this geometric filtering to the linear modelling by eliminating the modelling error, considered as a non-desired output signal component, in order to determine the model coefficients in the case of a linear modelling, linear model identification, and auto-regressive modelling. In addition, using Pythagoras theorem, we calculate the modelling error variance which can be used for testing the linear model approximation quality.
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Keywords: Geometric linear filtering, Gram-Schmidt orthogonalization, orthogonal component, geometric hyper plane, linear model, auto-regressive model
Pages: 75-85
WSEAS Transactions on Signal Processing, ISSN / E-ISSN: 1790-5052 / 2224-3488, Volume 10, 2014, Art. #8