Design of Filter Banks/Wavelets Using TROV: A Survey

Tay, D.B.H.

doi:10.1006/dspr.1997.0296

Cited by 14 publications

(9 citation statements)

References 32 publications

(59 reference statements)

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“…The wavelet filters considered in this paper belong to the class of HPFB [10], [15]. The lowpass filters are given by…”

Section: The Class Of Filter Bankmentioning

confidence: 99%

“…By Theorem 1, f num α l and f den α l are linear in the α l 's and can be computed from (14) and (10) by using the chain rule of derivatives. Equation (15) is nonlinear in the α l 's and would be difficult to solve in general. To overcome this difficulty, we propose an iterative procedure for the solution of equation (15).…”

Section: Optimization Strategymentioning

confidence: 99%

“…Equation (15) is nonlinear in the α l 's and would be difficult to solve in general. To overcome this difficulty, we propose an iterative procedure for the solution of equation (15). A linearization process is performed on equation (15) by letting f num = A and f den = B, where A and B are constants at each iteration.…”

Section: Optimization Strategymentioning

confidence: 99%

“…The purpose of linearization is to assist in the formulation of an algorithm to solve equation (15). As long as (15) is satisfied, optimality is achieved and it does not matter how the equation was solved.…”

Section: At the Kth Iteration Computementioning

confidence: 99%

“…The wavelet filters have a prescribed vanishing moments (number of zeros at z = −1) condition and are optimized with respect to the BU metric. The HPFB [10], [15] has many attractive features, including structural PR, efficient implementation, and simple design [10]. The lowpass analysis filter of the HPFB is a halfband filter.…”

Section: Introductionmentioning

confidence: 99%

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Balanced-Uncertainty Optimized Wavelet Filters with Prescribed Vanishing Moments

Tay

2004

Circuits, Systems, and Signal Processing

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In this paper, a localization measure that represents a balance between time and frequency localizations, called the Heisenberg balanced-uncertainty metric, is used for designing a class of wavelet filters. The filter banks belong to the class of halfband pair filter banks and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The optimization problem is shown to be the minimization of a ratio of quadratic functions, and an efficient technique for finding the solution is presented. Filters with different degrees of balance between time and frequency localizations can be designed with ease. Some interesting aspects of the localization measure of filters are also discussed.

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“…The wavelet filters considered in this paper belong to the class of HPFB [10], [15]. The lowpass filters are given by…”

Section: The Class Of Filter Bankmentioning

confidence: 99%