DWTs are constantly used to solve and treat more and more advanced problems. The
DWT algorithms were initially based on the compactly supported conjugate
quadrature filters (CQFs). However, a drawback in CQFs is due to the nonlinear phase
effects such as spatial dislocations in multi-scale analysis. This is avoided in
biorthogonal discrete wavelet transform (BDWT) algorithms, where the scaling and
wavelet filters are symmetric and linear phase. The biorthogonal filters are usually
constructed by a ladder-type network called lifting scheme. Efficient lifting BDWT
structures have been developed for microprocessor and VLSI environment. Only
integer register shifts and summations are needed for implementation of the analysis
and synthesis filters. In many systems BDWT-based data and image processing tools
have outperformed the conventional discrete cosine transform (DCT) -based
approaches. For example, in JPEG2000 Standard the DCT has been replaced by the
lifting BDWT.
A difficulty in multi-scale DWT analyses is the dependency of the total energy of the
wavelet coefficients in different scales on the fractional shifts of the analysed signal.
This has led to the development of the complex shift invariant DWT algorithms, the
real and imaginary
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