In this paper a new class of orthonormal functions which includes as particular case the Laguerre filters are introduced. These functions are defined as the product of a fixed transfer function of order n and of an all-pass filter of order n × h for any n and h. The orthogonality of these functions is proven in the general case. Moreover, the singular values of the sum of the first Nh members of this class are shown to be all equal to the orthonormalization constant.
A class of generalized orthonormal functions
XIBILIA, Maria Gabriella
2013-01-01
Abstract
In this paper a new class of orthonormal functions which includes as particular case the Laguerre filters are introduced. These functions are defined as the product of a fixed transfer function of order n and of an all-pass filter of order n × h for any n and h. The orthogonality of these functions is proven in the general case. Moreover, the singular values of the sum of the first Nh members of this class are shown to be all equal to the orthonormalization constant.File in questo prodotto:
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