Characterization of polynomials satisfying the super-Haar condition

Addison B. Jump; Harold H. Szu; Steven E. Noel

doi:10.1117/12.304861

26 March 1998 Characterization of polynomials satisfying the super-Haar condition

Addison B. Jump, Harold H. Szu, Steven E. Noel

Proceedings Volume 3391, Wavelet Applications V; (1998) https://doi.org/10.1117/12.304861
Event: Aerospace/Defense Sensing and Controls, 1998, Orlando, FL, United States

Abstract

The scaling function for the Super Haar wavelet is a linear combination of shifts in the Haar scaling function; the coefficients of this linear combination are assumed to be integers. If the scaling function satisfies the dilation equation the coefficients are said to be Super Haar Admissible. It has been shown that the z transform of Super Haar Admissible coefficients results in a polynomial that satisfies certain conditions. We define a related condition, which we call the Super Haar Condition and show that cyclotomic polynomials of odd order satisfy it. Further, dilation coefficients associated with such polynomials can immediately be found from relations among the cyclotomic polynomials. Using these results, a large class of Super Haar Admissible coefficients is identified and we conjecture that this class includes all admissible coefficients. We discuss applications to denoising and present an example.

Citation Download Citation

Addison B. Jump, Harold H. Szu, and Steven E. Noel "Characterization of polynomials satisfying the super-Haar condition", Proc. SPIE 3391, Wavelet Applications V, (26 March 1998); https://doi.org/10.1117/12.304861

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