Oblique generalizations of the Walsh basis
DOI:
https://doi.org/10.3103/S0735272710120010Keywords:
digital signal processing, discrete transform, generalized Walsh function, non-orthogonal Walsh discrete function, non-orthogonal discrete Walsh transformAbstract
An approach to building generalized oblique discrete Walsh basis is suggested. Methods that allow forming transformation matrices based on oblique discrete Walsh functions are developed. Some properties of the suggested oblique discrete Walsh transformations and their applications to synthesizing algorithms of parametric estimation of polynomial trend models of digital signals are considered.
References
H. F. Harmuth, Sequency Theory: Foundations and Applications (Academic, New York, 1977; Mir, Moscow, 1980).
E. Ye. Dagman and G. А. Kukharev, Fast Discrete Orthogonal Transforms (Nauka, Novosibirsk, 1983) [in Russian].
B. I. Golubov, А. V. Yefimov, and V. А. Skvortsov, Walsh Series and Transforms: Theory and Application (Izdat. LKI, Moscow, 2008) [in Russian].
I. I. Ismagilov, “Inclined Rademacher functions: properties and application in digital signal processing problems,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 39(12), 11 (1996); Radioelectron. Commun. Syst. 39(12), 9 (1996).
I. I. Ismagilov, “Discrete transforms in basis of piecewise-power functions and their properties,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 44(3), 54 (2001); Radioelectron. Commun. Syst. 44(3), 46 (2001).
I. I. Ismagilov, “On one generalization of discrete Rademacher functions,” Reports of Uzbekistan Republic Academy of Sciences, No. 8, 16 (1996).
L. А. Gnativ, А. D. Kozhuhovskiy, and А. I. Litvin, “Fast transform algorithms for Reed-Miller and Hamming codes,” Avtomatika, No. 4, 74 (1990).
I. I. Ismagilov, “An Approach to Ordering of Systems of the Walsh Discrete Functions,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 49(1), 65 (2006); Radioelectron. Commun. Syst. 49(1), 55 (2006).
I. I. Ismagilov, Discrete Transforms in Basis of Walsh-Like Functions: Theory and Application in Digital Signal Processing (Otechestvo, Kazan, 2003) [in Russian].
Yu. М. Smirnov, G. N. Vorobyov, Ye. S. Potapov, and I. I. S’uzev, Design of Specialized Information-Processing Systems (Vyssh. Shkola, Moscow, 1984) [in Russian, ed. by Yu. М. Smirnov].
I. Vuchkov, L. Boyadzhiyeva, and Ye. Solakov, Applied Linear Regression Analysis (Finansy i Statistika, Moscow, 1987) [in Russian].
S. L. Marple, Jr., Digital Spectral Analysis with Applications (Prentice-Hall, New Jersey, 1987; Mir, Moscow, 1990).
