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The Discrete Periodic Wavelet Transform in 1D

James F. Scholl
Organization: Rockwell Science Center
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A Mathematica package (Wavelet1Dv1.m) of a perfect reconstruction version of the fast wavelet transform (FWT) is presented here along with a notebook (Wavelet1Dv1.nb) illustrating its use. This version of the FWT called the discrete periodic wavelet transform (DPWT) was developed by N. Getz in 1992 (Memo. No. UCB/ERL M92/138, Electronics Research Lab. U. of California, Berkeley, CA 94720), and is based on circular convolution. The DPWT requires no data padding and the filter coefficients representing the wavelet basis system are adaptively modified to have the same length of a data set, if that data set is shorter than the array of filter coefficients. As a result of these improvements, the DPWT is invertible to as many number of decomposition levels as possible (L if the length of the data is 2^L). Also more types of orthogonal wavelet basis systems represented by longer length bandpass filters can be used. The only (minor) drawback is that even length filters can be used in the DPWT if the maximum number of levels of signal decomposition are desired. The enclosed notebook presents a couple of interesting examples of this package's use.

*Applied Mathematics > Numerical Methods > Approximation Theory > Wavelets
*Engineering > Electrical Engineering
*Engineering > Signal Processing

Subband Coding, Wavelet Transforms
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Wavelet1Dv1.m (9.9 KB) - Mathematica Package
Wavelet1Dv1.nb (311.8 KB) - Example Notebook for Wavelet1Dv1.m

Files specific to Mathematica 2.2 version:
Wavelet1Dv1.m (13.9 KB) - Mathematica Package
Wavelet1Dv1.ma (97.7 KB) - Example Notebook for Wavelet1Dv1.m