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   -> Volume 2, Issue 8

Preprint available: Dip Bounds for the 2D Wavelet Transform
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Jack K. Cohen, University of Colorado

PostPosted: Fri Nov 29, 2002 3:30 pm    
Subject: Preprint available: Dip Bounds for the 2D Wavelet Transform
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Preprint available: Dip Bounds for the 2D Wavelet Transform

Quantitative Dip Bounds for the Two-Dimensional Discrete Wavelet Transform

Jack K. Cohen and Tong Chen

An analysis of the discrete wavelet transform of dipping segments
with a signal of given frequency band leads to a Em{quantitative}
explanation of the known division of the two-dimensional wavelet
transform into horizontal, vertical and diagonal emphasis panels.
The results must be understood in a ``fuzzy" sense: since wavelet
mirror filters overlap, the results stated can be slightly violated
with violation tending to increase with shortness of the wavelet

The specific angles that delimit the three wavelet panels can be
stated in terms of the Nyquist frequency $F_t$ in the first dimension
and the Nyquist frequency $F_x$ in the second dimension. The angle
$ heta_{HV}=arctan(F_t/F_x)$ approximately separates the dips
$ heta< heta_{HV}$ that appear in the horizontal panel from those
greater dips that appear in the vertical panel. Similarly, the
angles $arctan(F_t/2F_x)$, $arctan(2F_t/F_x)$ approximately bound
the dips appearing in the diagonal panel. These results are simple
and probably have been observed by other researchers, but we haven't
found a prior reference for them.

The entire paper is available from our anonymous ftp site:,
in the directory pub/papers/wavelets.
There are 2 versions and to
accommodate different printing devices.

Jack K. Cohen,
University of Colorado
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