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Generalized Functions and Hartley Transforms in Number Systems with a Permanent Base

Authors: Syuzev V.V. Published: 08.04.2014
Published in issue: #2(95)/2014  
DOI:

 
Category: Informatics & Computing Technology  
Keywords: basis function, a basis system, Fourier transform, spectral analysis, number system

To solve the problems of digital signal processing in the spectral domain, a new method for analytical synthesis of discrete real parametric basis functions is proposed that uses the Hartmut procedure generalization to the case of number systems with an arbitrary constant-value basis. The mathematical description of functions obtained is given; their basic properties and methods for construction of different orthogonal-basis systems and transformations on their basis are investigated. In terms of these functions, all the basic theorems of spectral analysis used in the theory and practice of digital processing are formulated and proved. The obtained results are original and form the basis of theory of the signal representation and conversion in the new orthogonal basis.

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