A multivariable optimization problem is set to design 2-band PR-QMFs in this paper. The energy compaction, aliasing energy, step response, zero-mean high-pass filter, uncorrelated subband signals, constrained nonlinearity of the phase-response, and the given input statistics are simultaneously considered in the proposed optimal filter design technique. A set of optimal PR-QMF solutions and their optimization criteria along with their energy compaction performance are given for comparison. This approach of PR-QMF design leads to an input driven adaptive subband filter bank structure. It is expected that these optimal filters outperform the well-known fixed PR-QMFs in the literature for image and video coding applications.
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Çağlar et al. (1991) studied this question.
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