p-stage discrete orthonormalized and biorthonormalized wavelet basis for description of signals and linear nonstationary discrete control systems on the segment [0, L–1]

Technical cybernetics. Information technology. Computer facilities


Аuthors

Rybin V. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: dep805@mai.ru

Abstract

The spectral method [1-4] was developed for analysis and synthesis of nonstationary continuous, discrete, and continuous-discrete control systems. In the last decade, the wavelet transform is used widely in digital signal processing [5, 6, 7-9]. Wavelet transform is liked to Fourier transform, but it describes better the local features of functions in the spectral domain. A wavelet application for linear nonstationary control system analysis is discussed in [10, 11-12]. In [11] the discrete wavelets are constructed by continuous wavelet discretization. In [8] the construction algorithm of p-stage discrete orthonormalized wavelet basis on the segment   is suggested.
In this paper the construction algorithms for p-stage discrete orthonormalized and biorthonormalized wavelet basis are considered. Its realization in the MLSY_SM extension package [11, 12] for Mathcad is shown.

Keywords:

Biorthogonal wavelet bases; p-stage wavelet basis; non-stationary automatic control systems; spectral form of the mathematical description; mathematical computer-oriented systems


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