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   -> Volume 2, Issue 1

Technical Memorandum available
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Author Message
Neil Getz, University of California at Berkeley

PostPosted: Tue Dec 22, 1992 8:20 pm    
Subject: Technical Memorandum available
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Technical Memorandum available

A Fast Discrete Periodic Wavelet Transform

Neil Getz
Department of Electrical Engineering and Computer Sciences
Electronics Research Laboratory
University of California
Berkeley, California 94720

email: getz@robotics.Berkeley.EDU


The discrete wavelet transform (DWT) is extended to functions
on the discrete circle to create a fast and complete discrete
periodic wavelet transform (DPWT) for bounded periodic sequences.
This extension also solves the problem of non-invertibility that
arises in the application of the DWT to finite dimensional sequences
as well as provides the proper theoretical setting for previous
incomplete solutions to the invertibility problem. It is shown how and
proven that the same filter coefficients used with the DWT to create
orthonormal wavelets on compact support in the space of square summable
sequences over the integers may be incorporated through the DPWT to
create an orthonormal basis of discrete periodic wavelets. By exploiting
transform symmetry and periodicity, easily implementable and fast
synthesis and analysis algorithms are derived. Matlab functions for DPWT
experimentation are included.

Electronics Research Laboratory technical memo M92/138.

Requests for a copy of this memo may be sent to the author
via email to getz@robotics.Berkeley.EDU.
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