THEORY OF ORTHONORMAL M-BAND WAVELET PACKETS

In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the performance of wavelets for time-frequency localization, which makes more kinds of signals for analyzing by wavelets. Similar to the notations from the extension of 2-band wavelets to 2-band wavelet packets, the theoretic 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.     

M带正交子波包理论

M带正交子波基由于所具有的优良特性得到了广泛关注。2带子波包具有划分较高频率倍频程的能力,可用于改善子波对时间-频率局部化的性能,推广了信号的适用范围。本文用类似于从2带正交子波基扩展到2带子波包的概念,建立了M带子波包的的理论框架,并把有关2带子波包的定义、概念和性质推广到一般的M带子波包,给出了相应的证明。     

A NEW DE-NOISING METHOD BASED ON 3-BAND WAVELET AND NONPARAMETRIC ADAPTIVE ESTIMATION

Wavelet de-noising has been well known as an important method of signal de-noising. Recently,most of the research efforts about wavelet de-noising focus on how to select the threshold,where Donoho method is applied widely. Compared with traditional 2-band wavelet,3-band wavelet has advantages in many aspects. According to this theory,an adaptive signal de-noising method in 3-band wavelet domain based on nonparametric adaptive estimation is proposed. The experimental results show that in 3-band wavelet domain,the proposed method represents better characteristics than Donoho method in protecting detail and improving the signal-to-noise ratio of reconstruction signal.     

一种新的信号去噪方法及在激光信号中的应用

小波去噪是信号去噪的主要方法之一,目前的研究主要集中于如何选取阈值使去噪达到较好的效果,其中Donoho的阈值方法应用广泛.与传统双通道小波变换相比,三通道小波变换具有很多优势.基于这一理论,结合非参数自适应估计,推导出了一种适用于三通道小波域的自适应的信号去噪方法.实验证明,与三通道小波域中基于Donoho方法的去噪相比,该方法可以更好地保护细节以及提高重建信号的信噪比,在激光超声信号处理中也表现出良好的性能.     

Theory of regular M-band wavelet bases

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length K-regular 2-band wavelets of Daubechies (1988) to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Second, two approaches to the construction of the (M-1) wavelet filters and associated wavelet bases are described; one relies on a state-space characterization with a novel technique to obtain the unitary wavelet filters; the other uses a factorization approach. Third, this paper gives a set of necessary and sufficient condition on the M-band scaling filter for it to generate an orthonormal wavelet basis. The conditions are very similar to those obtained by Cohen (1990) and Lawton (1990) for 2-band wavelets     

Cyclic wavelet transforms for arbitrary finite data lengths

Multiresolution analysis via decomposition into wavelets has been established as an important transform technique in signal processing. A wealth of results is available on this subject, and particularly, the framework has been extended to treat finite length sequences of size 2ⁿ (for positive integers n) over finite fields. The present paper extends this idea further to provide a framework for dealing with arbitrary finite data lengths. This generalization is largely motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Here we extend the previous two-band formulation of the transform to treat a p-band case in general (i.e. for data length pⁿ), where p is a prime number, and we also give a general result for developing transforms over composite-length sequences. Potential applications and computational complexity issues are discussed as well.     

多母小波自适应小波滤波器

利用自适应小波变换（AWT）能融合不同母小波的优点,采用盖伯母小波和墨西哥帽母小波构成自适应小波.以光学人脸识别中降噪问题为应用背景,使用神经网络法对小波参数和组合系数进行优化,将生成的多母小波自适应小波滤波器用作人脸特征提取器.对噪声图像做特征提取,进行相关识别,采用3个指标定量分析识别结果.同盖伯小波和墨西哥帽小波识别结果的比较表明,多母小波自适应小波具有不同母小波的优点,并有良好的降噪性能.     

基于小波变换/小波包变换的多载波调制技术

小波/小波包在通信系统中的应用是近年来一个新的研究领域,而基于小波/小波包变换的多载波调制技术是其中一大研究热点。由于小波/小波包基函数具有良好的正交性与时频局域性等特点,基于小波/小波包变换的多载波调制技术,能够有效地提高通信系统性能。本文介绍了当前几种主要的基于小波/小波包变换的多载波调制方案,分析了这些方案的性能特点及发展趋势,并与其他方案进行了比较。     

Numerical solutions for orthogonal wavelet filters by Newton method

The wavelet transform has recently generated much interest in applied mathematics, signal processing and image coding. Mallat (1989) used the concept of the function space as a bridge to link the wavelet transform and multiresolution analysis. Daubechies (1990) added regularity conditions to find 2N, 2N10, tap coefficients for orthogonal wavelet filters. Owing to the difficulty of finding their closed solutions for large N a numerical method called the Newton method is proposed. We constructed the orthogonal wavelet filter with 2N-tap coefficients by N linear equations and N nonlinear equations. The 2N-tap, 2N10, coefficients we found are very consistent with those of Daubechies. Also, the method can be used to find the orthogonal wavelet filter with N-tap coefficients for N>10.     

A new approach for designing orthogonal wavelets for multicarrier applications

The Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER, behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced. The Cramer–Rao lower bound is applied to access the BER performance of the proposed wavelet.