Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

İlker Bayram; Ivan W. Selesnick

doi:10.1117/12.741073

2 October 2007 Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

İlker Bayram, Ivan W. Selesnick

Proceedings Volume 6763, Wavelet Applications in Industrial Processing V; 67630H (2007) https://doi.org/10.1117/12.741073
Event: Optics East, 2007, Boston, MA, United States

Abstract

Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for time-scale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechies-type filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet wavelet transforms (tight frames) with FIR filters obtained using matrix spectral factorization.

Citation Download Citation

İlker Bayram and Ivan W. Selesnick "Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors", Proc. SPIE 6763, Wavelet Applications in Industrial Processing V, 67630H (2 October 2007); https://doi.org/10.1117/12.741073

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