Simplified equations to generate wavelets of arbitrary order of regularity

Addison B. Jump; Barry G. Sherlock

doi:10.1117/12.421220

26 March 2001 Simplified equations to generate wavelets of arbitrary order of regularity

Addison B. Jump, Barry G. Sherlock

Proceedings Volume 4391, Wavelet Applications VIII; (2001) https://doi.org/10.1117/12.421220
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

This research deals with finite length, perfect reconstruction two-channel orthonormal wavelet filters. We have previously derived equations that allow the user to set the regularity of these filters to any value between one and the maximum possible. These equations were extremely involved and intricate. We derive identities that greatly simplify the equations and reduced computational complexity. We indicate how the equations may be used to find the optimum filter for a particular application over a pool of filters of regularity set by the user. We advance conjectures as to the theoretical significant of the structure of these equations and discuss numerical solutions.

Citation Download Citation

Addison B. Jump and Barry G. Sherlock "Simplified equations to generate wavelets of arbitrary order of regularity", Proc. SPIE 4391, Wavelet Applications VIII, (26 March 2001); https://doi.org/10.1117/12.421220

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