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Wavelet packets and wavelet frame packets on local fields  [PDF]
Biswaranjan Behera,Qaiser Jahan
Mathematics , 2011,
Abstract: Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this lemma we have constructed the wavelet packets associated with such MRAs. We show that these wavelet packets generate an orthonormal basis by translations only. We also prove an analogue of splitting lemma for frames and construct the wavelet frame packets in this setting.
Some Results on Wavelet Frame Packets  [PDF]
Sana Khan, Mohammad Kalimuddin Ahmad
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.411069
Abstract: The aim of this paper is to study wavelet frame packets in which there are many frames. It is a generalization of wavelet packets. We derive few results on wavelet frame packets and have obtained the corresponding frame bounds.
The Characteristics of Orthogonal Trivariate Wavelet Packets  [PDF]
Qingjiang Chen,Zongtian Wei
Information Technology Journal , 2009,
Abstract: The notion of orthogonal nonseparable trivariate wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. An approach for constructing them is presented. Their orthogonality properties are discussed. Three orthogonality formulas concerning these wavelet packets are obtained. The orthonormal bases of space L2 (R3) is presented.
A Study on B-Spline Wavelets and Wavelet Packets  [PDF]
Sana Khan, Mohammad Kalimuddin Ahmad
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.519287
Abstract: In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.
Wavelets and Wavelet Packets on Quantum Computers  [PDF]
Andreas Klappenecker
Physics , 1999, DOI: 10.1117/12.366826
Abstract: We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.
Construction of Biorthogonal Wavelet Packets on Local Fields of Positive Characteristic  [PDF]
F. A. Shah,M. Y. Bhat
Mathematics , 2014,
Abstract: Orthogonal wavelet packets lack symmetry which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by the biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of the Fourier transforms. We also show how to obtain several new Riesz bases of the space L2(K) by constructing a series of subspaces of these wavelet packets. Finally, we provide the algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.
Simulation of Gegenbauer Processes using Wavelet Packets  [PDF]
Jér?me Collet,Jalal Fadili
Mathematics , 2006,
Abstract: In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and Wickerhauser [1], to adaptively search for the best-ortho-basis in the wavelet packet library where the covariance matrix of the transformed process is nearly diagonal. Our method clearly outperforms the one recently proposed by [2], is very fast, does not depend on the wavelet choice, and is not very sensitive to the length of the time series. From these first results we propose an algorithm to build bases to simulate k-factor Gegenbauer processes. Given its practical simplicity, we feel the general practitioner will be attracted to our simulator. Finally we evaluate the approximation due to the fact that we consider the wavelet packet coefficients as uncorrelated. An empirical study is carried out which supports our results.
THEORY OF M-BAND WAVELET PACKETS
M带正交子波包理论

Zhang Jiankang,Bao Zheng,Jiao Licheng,
张建康
,保铮,焦李成

电子与信息学报 , 1998,
Abstract: In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the properpty of wavelet for time-frequency localization, which makes more kinds of signals for analyzing by wavelet. Similar to the notations from the extention of 2-band wavelets to 2-band wavelet packets, the theory framework of M-band wavelet packets is developed, a generalization of the notations and properties of 2-band wavelet packets to that of M-band wavelet packets is made and the corresponding proofs are given.
Selection of Mother Wavelet For Image Compression on Basis of Nature of Image  [cached]
Gajanan K. Kharate,Varsha H. Patil,Niranjan L. Bhale
Journal of Multimedia , 2007, DOI: 10.4304/jmm.2.6.44-51
Abstract: Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The results of the compression change as per the basis and tap of the wavelet used. This paper compares compression performance of Daubechies, Biorthogonal, Coiflets and other wavelets along with results for different frequency images. Based on the result, it is proposed that proper selection of mother wavelet on the basis of nature of images, improve the quality as well as compression ratio remarkably. The prime objective is to select the proper mother wavelet during the transform phase to compress the color image. This paper includes the discussion on principles of image compression, image compression methodology, the basics of wavelet and orthogonal wavelet transforms, the selection of discrete wavelet transform with results and conclusion.
Combined Wavelet Packets and Best Bases
混合小波包与最佳基

CHEN Yu-yu,CHEN Yu-yu,WANG Guo-yi,
陈玉宇
,张 钹,王国意

软件学报 , 1998,
Abstract: In this paper, the concept of CWP(combined wavelet packets) is proposed. CWP can be obtained from COWB(combined orthonormal wavelet bases) which is composed of several orthonormal wavelet bases having the same space structure in a multiresolution analysis view. Compared with traditional wavelet packets, CWP have not only better frequency localization, but also waveshape variation. The wavelet coefficients can be computed by a fast algorithm which computes in the frequency domain and uses FFT.
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