基于规范正交小波的自适应均衡器

本文在分析传统均衡器性能的基础上,提出了一种基于小波分析的均衡器OWBE,用一组规范正交小波及其对应的一组系数来表示均衡器。文中给出了自适应算法,并对算法性能做了简要分析.与基于LMS算法的横向均衡器(LTE)相比,OWBE收敛速度快,而计算量增加很少,易于实时实现.     

经典规范正交子波的一种简单广义化方法及其应用

从最简单的Haar尺度函数入手，提出一种简单而又快捷的方法，将每一个经典的规范正交子波基进行拓展得到一类新的规范正交子波基。新子波类中的每一个子波均继承了原始子波的许多基本性质，比如规范正交性，正则阶，时、频局域化特性等，同时也得到某些性能的改善，文中重点探讨广义Haar子波、广义Shannon子波和Meyer子波、Daubechies子波等的简单广义化；最后讨论新子波系统的一个直接应用：实（序列）信号解析子波变换的快速算法问题。     

光滑正交小波库的构造及在信号去噪中的应用

针对实际应用中小波的多样性要求，提出应用构造光滑正交小波库的方法来解决这个矛盾，光滑正交小波库是基于规则性、非冗余性、完备性进行构造。文中把构造好的小波库应用到信号去噪中，实验结果证明，在绝大多数情况下基于正交小波库的去噪方法性能优于任何一种单一的小波。     

Orthonormal wavelets with simple closed-form expressions

Two classes of orthonormal wavelets that have simple closed-form expressions are derived from pulses with the raised-cosine spectrum. These wavelets, which are bandlimited and polynomial-decaying in time, are found to be particular examples of the Lemarie-Meyer (1992, 1993) wavelets. The derivation reveals interesting connections between wavelet construction and intersymbol interference (ISI)-free signaling for digital communications     

Examples of bivariate nonseparable compactly supported orthonormalcontinuous wavelets

We give many examples of bivariate nonseparable compactly supported orthonormal wavelets whose scaling functions are supported over [0,3]x[0,3]. The Holder continuity properties of these wavelets are studied.     

A new design algorithm for two-band orthonormal rational filterbanks and orthonormal rational wavelets

We present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (e,g., regularity). Although the filters obtained from this algorithm are suboptimally designed, they show excellent frequency selectivity. After an in-depth account of the algorithm, we discuss the properties of the rational wavelets generated by some designed filters. In particular, we stress the possibility to design “almost” shift error-free wavelets, which allows the implementation of a rational wavelet transform     

On solving first-kind integral equations using wavelets on abounded interval

The conventional method of moments (MoM), when applied directly to integral equations, leads to a dense matrix which often becomes computationally intractable. To overcome the difficulties, wavelet-bases have been used previously which lead to a sparse matrix. The authors refer to “MoM with wavelet bases” as “wavelet MoM”. There have been three different ways of applying the wavelet techniques to boundary integral equations: 1) wavelets on the entire real line which requires the boundary conditions to be enforced explicitly, 2) wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line, and 3) “wavelet-like” basis functions. Furthermore, only orthonormal (ON) bases have been considered. The present authors propose the use of compactly supported semi-orthogonal (SO) spline wavelets specially constructed for the bounded interval in solving first-kind integral equations. They apply this technique to analyze a problem involving 2D EM scattering from metallic cylinders. It is shown that the number of unknowns in the case of wavelet MoM increases by m-1 as compared to conventional MoM, where m is the order of the spline function. Results for linear (m=2) and cubic (m=4) splines are presented along with their comparisons to conventional MoM results. It is observed that the use of cubic spline wavelets almost “diagonalizes” the matrix while maintaining less than 1.5% of relative normed error. The authors also present the explicit closed-form polynomial representation of the scaling functions and wavelets     

Multiresolution wavelet analysis of evoked potentials

Neurological injury, such as from cerebral hypoxia, appears to cause complex changes in the shape of evoked potential (EP) signals. To characterize such changes we analyze EP signals with the aid of scaling functions called wavelets. In particular, we consider multiresolution wavelets that are a family of orthonormal functions. In the time domain, the multiresolution wavelets analyze EP signals at coarse or successively greater levels of temporal detail. In the frequency domain, the multiresolution wavelets resolve the EP signal into independent spectral bands. In an experimental demonstration of the method, somatosensory EP signals recorded during cerebral hypoxia in anesthetized cats are analyzed. Results obtained by multiresolution wavelet analysis are compared with conventional time-domain analysis and Fourier series expansions of the same signals. Multiresolution wavelet analysis appears to be a different, sensitive way to analyze EP signal features and to follow the EP signal trends in neurologic injury. Two characteristics appear to be of diagnostic value: the detail component of the MRW displays an early and a more rapid decline in response to hypoxic injury while the coarse component displays an earlier recovery upon reoxygenation     

Algorithms for designing wavelets to match a specified signal

Algorithms for designing a mother wavelet /spl psi/(x) such that it matches a signal of interest and such that the family of wavelets {2/sup -(j/2)//spl psi/(2/sup -j/x-k)} forms an orthonormal Riesz basis of L/sup 2/(/spl Rscr/) are developed. The algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum. Many applications require wavelets that are matched to a signal of interest. Most current design techniques, however, do not design the wavelet directly. They either build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a scaling function that generates a multiresolution analysis with some desired properties. In this paper, two sets of equations are developed that allow us to design the wavelet directly from the signal of interest. Both sets impose bandlimitedness, resulting in closed form solutions. The first set derives expressions for continuous matched wavelet spectrum amplitudes. The second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum. The discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies. An interesting byproduct of this work is the result that Meyer's spectrum amplitude construction for an orthonormal bandlimited wavelet is not only sufficient but necessary. Specific examples are given which demonstrate the performance of the wavelet matching algorithms for both known orthonormal wavelets and arbitrary signals.     

Modified wavelets and their applications

Wavelets obtained from known orthonormal wavelets modified by the impulse response of a stationary linear system are proposed. It is shown that the new wavelets offer additional possibilities for signal processing in the presence of noise. In particular, these wavelets provide for estimation of linearly transformed signals and simultaneous suppression of the noise effect. Filter banks that realize fast computational algorithms are synthesized. The wavelet approach is exemplified by solution of deconvolution, decorrelation, and differentiation problems.     

Full wave analysis of microstrip floating line structures bywavelet expansion method

A full wave analysis of microstrip floating line structures by wavelet expansion method is presented. The surface integral equation developed from a dyadic Green's function is solved by Galerkin's method, with the integral kernel and the unknown current expanded in terms of orthogonal wavelets. Using the orthonormal wavelets (and scaling functions) with compact support as basis functions and weighting functions, the integral equation is converted into a set of linear algebraic equations, with the matrices nearly diagonal or block-diagonal due to the localization, orthogonality, and cancellation properties of the orthogonal wavelets. Limitations inherited in the traditional orthogonal basis systems are released: The problem-dependent normal modes have been replaced by the problem-independent wavelets, preserving the orthogonality; the trade-off between orthogonality and continuity (e.g. subsectional basis functions including pulse functions, roof-top functions, piecewise sinusoidal functions, etc.) is well balanced by the orthogonal wavelets. Numerical results are compared with measurements and previous published data with good agreement     

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.     

Wavelets and recursive filter banks

It is shown that infinite impulse response (IIR) filters lead to more general wavelets of infinite support than finite impulse response (FIR) filters. A complete constructive method that yields all orthogonal two channel filter banks, where the filters have rational transfer functions, is given, and it is shown how these can be used to generate orthonormal wavelet bases. A family of orthonormal wavelets that have a maximum number of disappearing moments is shown to be generated by the halfband Butterworth filters. When there is an odd number of zeros at π it is shown that closed forms for the filters are available without need for factorization. A still larger class of orthonormal wavelet bases having the same moment properties and containing the Daubechies and Butterworth filters as the limiting cases is presented. It is shown that it is possible to have both linear phase and orthogonality in the infinite impulse response case, and a constructive method is given. It is also shown how compactly supported bases may be orthogonalized, and bases for the spline function spaces are constructed     

Bandwidth efficient PAM signaling using wavelets

In this article, we demonstrate a bandwidth efficient method of pulse amplitude modulation (PAM) signaling using a family of orthonormal wavelets as the baseband pulse. These wavelets can be transmitted using single sideband (SSB) transmission, since they have zero average value. We provide a comparison with raised-cosine signaling, with the wavelet approach offering 50% greater data rate at the same bandwidth     

Multiscale Wiener filter for the restoration of fractal signals:wavelet filter bank approach

A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals     

On cosine-modulated wavelet orthonormal bases

Multiplicity M, K-regular, orthonormal wavelet bases (that have implications in transform coding applications) have previously been constructed by several authors. The paper describes and parameterizes the cosine-modulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs, the scaling function uniquely determines the wavelets. This is in contrast to the general multiplicity M case, where one has to, for any given application, design the scaling function and the wavelets. Several design techniques for the design of K regular cosine-modulated WTFs are described and their relative merits discussed. Wavelets in K-regular WTFs may or may not be smooth, Since coding applications use WTFs with short length scaling and wavelet vectors (since long filters produce ringing artifacts, which is undesirable in, say, image coding), many smooth designs of K regular WTFs of short lengths are presented. In some cases, analytical formulas for the scaling and wavelet vectors are also given. In many applications, smoothness of the wavelets is more important than K regularity. The authors define smoothness of filter banks and WTFs using the concept of total variation and give several useful designs based on this smoothness criterion. Optimal design of cosine-modulated WTFs for signal representation is also described. All WTFs constructed in the paper are orthonormal bases.     

On the use of Coifman intervallic wavelets in the method of momentsfor fast construction of wavelet sparsified matrices

Orthonormal wavelets have been successfully used as basis and testing functions for the integral equations and extremely sparse impedance matrices have been obtained. However, in many practical problems, the solution domain is confined in a bounded interval, while the wavelets are originally defined on the entire real line. To overcome this problem, periodic wavelets have been described in the literature. Nonetheless, the unknown functions must take on equal values at the endpoints of the bounded interval in order to apply periodic wavelets as the basis functions. We present the intervallic Coifman wavelets (coiflets) for the method of moments (MoM). The intervallic wavelets release the endpoints restrictions imposed on the periodic wavelets. The intervallic wavelets form an orthonormal basis and preserve the same multiresolution analysis (MRA) of other usual unbounded wavelets. The coiflets possesses a special property that their scaling functions have many vanishing moments. As a result, the zero entries of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. Further, the majority of matrix elements are evaluated directly without performing numerical integration procedures such as Gaussian quadrature. For an n×n matrix, the number of actual numerical integrations is reduced from n² to the order of 3n(2L-1), when the coiflets of order L is employed. The construction of intervallic wavelets is presented. Numerical examples of scattering problems are discussed and the relative error of this method is studied analytically     

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.     

用余弦调制PR－FIR方法构造正交小波基

离散小波变换将离散时间信号分解为一系列不同分辨率下的离散近似信号和离散细节，紧支的正交规范小波与完全重构正交镜象滤波器（ＰＲ－ＱＭＦ）相对应。本文在“二带”正交小波基的构造条件下，利用余弦调制完全重构滤波器组的方法，实现了正交小波基的构造，计算模拟表明该方法非常简单、有效。     

Image compression through embedded multiwavelet transform coding

In this paper, multiwavelets are considered in the context of image compression and two orthonormal multiwavelet bases are experimented, each used in connection with its proper prefilter. For evaluating the effectiveness of multiwavelet transform for coding images at low bit-rates, an efficient embedded coding of multiwavelet coefficients has been realized. The performance of this multiwavelet-based coder is compared with the results obtained for scalar wavelets.