An approach to ordering of systems of the Walsh discrete functions

I. I. Ismagilov

doi:10.3103/S0735272706010079

Authors

I. I. Ismagilov Kazan State Finance and Economics Institute, Russian Federation

DOI:

https://doi.org/10.3103/S0735272706010079

Abstract

A new approach is suggested to ordering of the Walsh discrete functions based on the properties of their finite-difference representations. The new relationships are used for generating a permutable sequence to construct the difference-ordered system of Walsh functions based on the Walsh-Paley system. Generalization of the Kronecker product of matrices permits to develop a technique of synthesis of the transformation matrix for another version of the difference-ordered system of Walsh functions.

References

AHMED, N.; RAO, K.R. Orthogonal Transforms for Digital Signal Processing. Springer-Verlag, 1975.

>2. DAGMAN, E.Y.; KUKHAREV, G.A. Fast Discrete Orthogonal Transforms [in Russian]. Novosibirsk: Nauka, 1983.

TRAKHTMAN, A.M.; TRAKHTMAN, V.A. Foundations of the Theory of Discrete Signals on Finite Intervals [in Russian]. Moscow: Sov. Radio, 1975.

SADYKHOV, R.K.; CHEGOLIN, P.M.; SHMERKO, V.P. Methods and Devices for Signal Processing in a Discrete Basis [in Russian]. Minsk: Nauka i Tekhnika, 1987.

BELETSKII, A.Y. The ordered Gray codes. Uspekhi Sovremennoy Radioelektroniki, n.11, p.3-22, 2003.

ISMAGILOV, I.I. Discrete Transformations in the Bases of Walsh-Like Functions — Theory and Applications in Signal Digital Processing [in Russian]. Kazan’: Otechestvo, 2003.

SMIRNOV, Y.M. (ed.). Design of Special-Purpose Information-and-Computation Systems [in Russian]. Moscow: Vysshaya Shkola, 1984.