Balanced-Uncertainty Optimized Wavelet Filters with Prescribed Vanishing Moments

Abstract

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.

A new approach to design triplet halfband filter banks based on balanced-uncertainty optimization

“…In [20], the better performance of image compression algorithms is shown by balancing time and frequency localizations of wavelet filters. In pioneering work [21], Tay introduced an optimization of a balanceduncertainty (BU) metric [20] using PBP to design a class of HPFB [5]. The designed filters have good balance of time-frequency localizations.…”

“…It has been addressed in [19][20][21][22][23] that the optimal FBs designed to achieve different balance between the time and frequency localizations are very effective in image compression, image segmentation and feature extraction algorithms. Moreover, the timefrequency localized optimization criteria has been used in the design of optimal HPFB.…”

“…In addition, the LHBF, Neville filter or MFHBF have limited flexibility in controlling the roll-off in frequency response of the wavelet filters [7]. Also, it is shown in [21] that increasing the length of LHBF or MFHBF does not necessarily give greater frequency localization.…”

“…The prescribed VMs are imposed to obtain the independent parameters α i of weighted Euler-Frobenius halfband polynomial. An efficient iterative technique in [21] is employed to obtain BU optimized parameter, β i . Next, these time-frequency localized HBFs are used in the THFB structure.…”

An integrated approach for structural damage identification using wavelet neuro-fuzzy model

“…For vibration response based structural damage identification methods, transmissibility measurements are always subject to environmental, operational and measurement variability, and the uncertainty will propagate through to any features derived from it, leading to misinterpretation and false alarms (Mao & Todd, 2012). Uncertainty caused by noise and variability has successfully been quantified with signal processing methods such as WT algorithm (Tay, 2004;Wu & Deng, 2008), ANFIS (Noori, Hoshyaripour, Ashrafi, & Araabi, 2010;Theodoridis, Boutalis, & Christodoulou, 2010) and interval modeling technique (Lew & Loh, 2012;Red-Horse & Paez, 2008). Furthermore, the incorporation of the three methods generates a better effect on identifying structural damage.…”