Unitary mappings between multiresolution analysis of L2(R) and a parameterization of low-pass filters

Manos Papadakis

doi:10.1117/12.255243

23 October 1996 Unitary mappings between multiresolution analysis of L²(R) and a parameterization of low-pass filters

Manos Papadakis

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255243
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

This paper examines classes of unitary operators of L²(R) contained in the commutant of the shift operator, such that for any pari of multiresolution analyses of L²(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We use these unitary operators to provide an interesting class of scaling functions. We show that the Dai-Larson unitary parameterization of orthonormal wavelets is not suitable for the study of scaling functions. These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L²([ -(pi) , (pi) ]), which we characterize. Using this characterization we recapture Daubechies' orthonormal wavelets by passing the spectral factorization process.

Citation Download Citation

Manos Papadakis "Unitary mappings between multiresolution analysis of L²(R) and a parameterization of low-pass filters", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255243

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