Glasnik matematički, Vol. 46 No. 2, 2011.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.46.2.11
A finite-dimensional approach to wavelet systems on the circle
Brody Dylan Johnson
; Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, USA
Sažetak
Motivated by recent developments in the study of finite-dimensional frames, this work develops an independent theory of finite-dimensional wavelet systems on the circle. Using natural translation and dilation operators, trigonometric polynomial, orthonormal scaling functions are constructed which give rise to finite-dimensional multiresolution analyses and, consequently, orthonormal wavelet systems. It is shown that the finite-dimensional systems so constructed can lead to arbitrarily close approximation of square-integrable functions on the circle. Departures from the existing theory of periodic wavelets are encountered, e.g., the finite-dimensional equivalent of the Smith-Barnwell equation describes both a necessary and sufficient condition on a candidate low-pass filter for the existence of an orthonormal scaling function. Moreover, this finite-dimensional framework allows for a natural analog to the Shannon wavelet, in contrast to the classical periodic wavelets.
Ključne riječi
Wavelet; circle; periodic wavelet; multiresolution analysis
Hrčak ID:
74269
URI
Datum izdavanja:
23.11.2011.
Posjeta: 875 *