Biorthogonal Wilson bases

Kai Bittner

doi:10.1117/12.366798

26 October 1999 Biorthogonal Wilson bases

Kai Bittner

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366798
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Wilson bases consist of products of trigonometric functions with window functions which have good time-frequency localization, so that the basis functions themselves are well localized in time and frequency. Therefore, Wilson bases are well suited for time-frequency analysis. Daubechies, Jaffard and Journe have given conditions on the window function for which the resulting Wilson basis is orthonormal. In particular, they constructed an example where the basis functions have exponential decay in the time and the frequency domain. Here, we investigate biorthogonal Wilson bases with arbitrary shape. Necessary and sufficient conditions for the Riesz stability of these bases are given. Furthermore, we determine exact Riesz bounds and the dual bases.

Citation Download Citation

Kai Bittner "Biorthogonal Wilson bases", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366798

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available