Abstract
A class of 4-band symmetric biorthogonal wavelet bases has been constructed, in which any wavelet system the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reversed for application requirement. Some concrete examples with high vanishing moments are also given, the properties of the transformation matrix are studied and the optimal model is constructed. These wavelets can process the boundary conveniently, and they lead to highly efficient computations in applications.
Highlights
As a generalization of orthogonal wavelets, the biorthogonal wavelets have become a fundamental tool in many areas of applied mathematics, from signal processing to numerical analysis [ – ]
Biorthogonal wavelets, multi-band wavelets are designed as alternatives for more freedom and flexibility [ – ]
We can construct innumerable wavelet filters with some structure for fast calculation, among which we can select the best ones for practical applications
Summary
As a generalization of orthogonal wavelets, the biorthogonal wavelets have become a fundamental tool in many areas of applied mathematics, from signal processing to numerical analysis [ – ]. In Section , we design a type of -band biorthogonal wavelets filters for fast calculation, give the construction method. For L = , an example of a filter bank {h, g , g , g } is as follows: This type of wavelet filter banks are only determined the two low-pass filters h, h, i.e., the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. It can reduce the computational complexity and facilitate fast computation. We relax the condition of the sum of highest vanishing moments, and let L = and the high-pass wavelet filters defined by
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