用于信号逼近的最佳正交子波选择方法

离散子波变换将离散时间信号分解为一系列分辨率下的离散逼近和离散细节，紧支的正交规范子波与完全重建正交镜象滤波器组相对应。本文提出一种用于信号最佳逼近的正交子波选择方法，即选择满足一定条件的滤波器的方法。通过对滤波器参数化，可以将带约束的最佳化问题转化为无约束最优化问题，通过对参数在一定范围内的搜索，得到最优解，文中给出了计算机模拟的结果。     

M带离散时间子波变换

二带连续时间子波变换可由无限级树形正交镜像滤波器(QMF)组产生,类似地,二带离散时间子波变换可表示为有限级树形QMF组。该文对二带离散时间子波变换进行了推广,给出了M带离散时间于波变换,并研究了M带离散时间子波变换与M带仿酉滤波器组之间的关系。结果表明,在L级M带树形滤波器组中,如果每级滤波器组是仿酉滤波器组,则该树形滤波器组所产生的离散时间子波基是正交基。     

M带离散时间子波变换

二带连续时间子波变换可由无限级树形正交镜像滤波器（ＱＭＦ）组产生,类似地,二带离散时间子波变换可表示为有限级树形ＱＭＦ组,该文对二带离散时间子波变换进行了推广,给出了Ｍ带离散时间子波变换,并研究了Ｍ带离散时间子波变换与Ｍ带仿酉滤波器组之间的关系。结果表明,在Ｌ级Ｍ带树形滤波器组中,如果每级滤波器组仿酉滤波器组,则该树形滤波器组所产生的离散时间子波基是正交基。     

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。     

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。     

一种高性能内插滤波器的设计

在全数字接收机系统中,随着高阶调制解调技术的应用,传统内插滤波器的性能已不能满足要求。为此,通过研究一种多项式函数的频率响应,提出了一种高性能内插滤波器的设计方法。该方法在频域逼近的基础上,以线性加权的最小均方误差（MMSE）为优化准则,利用Matlab系统函数进行线性约束条件下的最优化迭代,设计非常灵活。仿真结果表明,该方法设计的内插滤波器性能明显优于常用的内插滤波器,尤其适合于高阶正交幅度调制（QAM）信号。     

基于DSP的正交离散子波变换系统的设计与实现

子波变换现已成为一种重要的信号处理方法．本文提出一种以ＴＩ公司ＤＳＰ（ＴＭＳ３２０Ｃ３０）为基础的一维正交离散子波变换系统的实现方法，用该系统实现 Ｍａｌｌａｔ 正交子波快速分解与重构算法，并详细介绍了该系统的电路设计原理和相应的软件流程．测试结果表明该系统重构信号的绝对误差小于１０~( －３)。     

基于MM算法的脉冲串模糊函数设计方法

针对离散相位调制脉冲串信号的模糊函数优化问题,提出了一种基于MM算法的波形设计方法。MM算法是一种求解最优化问题的迭代算法,通过重复“构造辅助函数-求解辅助函数最优值”的过程,可以逐步逼近原问题的全局最优解。本文首先将脉冲串模糊函数设计问题建模为带约束四次型最优化问题,然后根据泰勒展开,给出了位于原函数上界的辅助函数的构造方法。其中,辅助函数的形式为带约束二次型最优化问题,可通过交替方向乘子法（ADMM）求解。最后通过计算机仿真说明了该方法的有效性。     

基于阈值决策的子波域去噪方法

通过对信号多尺度边缘滤波和Ｄｏｎｏｈｏ阈值决策子波域滤波方法（Ｃ－Ｄ方法）进行研究，首先给出了Ｃ－Ｄ阈值选取证明，推导了理论阈值，接着将Ｃ－Ｄ推广到非正交子波基，使其不仅适用于正交多分辨分解，亦适用于离散子波变换，本文对一维和二维信号的多种子波滤波算法进行了仿真计算，全面分析了Ｃ－Ｄ算法的性能。     

离散子波分解的专用芯片设计及CPLD实现

子波变换是信号处理和图像压缩等诸多领域中一个非常有效的数学分析工具。日前,其实现方式多为软件编程。本文针对子波变换与滤波器组的关系,在卷积滤波、下二采样过程中,将数据按一定规律重排,用复杂可编程逻辑器件(CPLD)设计了一种专用芯片(ASIC)可完成离散子波分解,具有一定的实用价值。     

Completeness of arbitrarily sampled discrete time wavelettransforms

An arbitrarily sampled discrete time wavelet transform is said to be complete if it is uniquely invertible, i.e., if the underlying signal can be uniquely recovered from the available samples of the wavelet transform. We develop easy-to-compute necessary and sufficient conditions and necessary but not sufficient conditions for the completeness of an arbitrarily sampled dyadic discrete time wavelet transform of a periodic signal. In particular, we provide necessary and sufficient conditions for completeness of the sampled wavelet transform when the lowpass filter associated with the dyadic wavelet filter bank has no unit circle zeros other than those at z=1. We present necessary but not sufficient conditions for completeness when the lowpass filter associated with the dyadic wavelet filter bank has arbitrary unit circle zeros. We also provide necessary and sufficient conditions for completeness of a set of samples of both the lowpass approximation to the signal and its wavelet transform. All the conditions we derive use only information about the location of the retained samples and the analyzing wavelet filter bank. They can easily be checked without explicitly computing of the rank of a matrix. Finally, we present a simple signal reconstruction procedure that can be used once we have determined the arbitrarily sampled discrete time wavelet transform is complete     

基于小波变换的话务量预测

本文将小波变换应用到话务量的预测中,利用小波分解法将非平稳时间序列的GSM话音话务量分解为多个细节信号分量和逼近信号分量。对细节信号采用AR模型或者余弦逼近进行拟合建模,对逼近信号采用多项式拟合和AR模型相结合的方式建模。利用某运营商2009年1月~2013年7月每月的博彩日话音话务作为检验序列集,前50个月的数据用来建模拟合,最后5个月数据作为预测比较,发现拟合相关度为0.991,预测平均绝对误差为0.029,预测结果比单纯使用曲线拟合要好。     

A Novel Algorithm for Robust Audio Watermarking in Wavelet Domain

With the sharp blossoming of the Internet, itbecomes more and more important to protect theintelligent property rights (IPR). Watermarking is aneffective solution. It takes advantage of the redundancyof the human visual system (HVS) and auditory system(HAS) to identify the copyright by embedding somesecret information relevant to IPR holders. The invisible watermarking algorithm shouldsatisfy the demands on imperceptivity, low complexity,robustness, determinacy and safety. However,imperc…     

From the wavelet series to the discrete wavelet transform-theinitialization

The discrete wavelet transform (DWT) is computed by subband filters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of improper initialized discretization of the continuous-time signal. In this correspondence, the problem is analyzed, and two simple algorithms for the initialization are introduced. Finally, numerical examples are presented to show that our algorithms are more effective than others     

重构小波系数的分段三次样条播值新算法

利用小波变换模极大值原理对信号去噪之后,如何由保留下来的模极大值点恢复出满意的重构信号,是一个重要课题。本文首先分析模极大值与小波系数之间的内在关系,提出了模极大值实际上是小波系数在特定意义下的离散采样;然后给出了一种对模极大值进行预处理的方法,由此得到了一组新的伪模极大值序列;利用这组伪模极大值序列,提出了一种新的重构小波系数的分段三次样条播值（ＰＣＳＩ）新算法,该算法程序简单,易实现,克服了交替投影（ＡＰ）法计算量大、程序复杂等缺点;最后给出一个应用实例,实验结果表明,与经典的交替投影法相比,本文提出的ＰＣＳＩ算法可获得更高的重构信号信噪比增益和更小的相对均方误差,它是一种实际、有效的算法。     

Efficient wavelet prefilters with optimal time-shifts

A wavelet prefilter maps sample values of an analyzed signal to the scaling function coefficient input of standard discrete wavelet transform (DWT) algorithms. The prefilter is the inverse of a certain postfilter convolution matrix consisting of integer sample values of a noninteger-shifted wavelet scaling function. For the prefilter and the DWT algorithms to have similar computational complexity, it is often necessary to use a "short enough" approximation of the prefilter. In addition to well-known quadrature formula and identity matrix prefilter approximations, we propose a Neumann series approximation, which is a band matrix truncation of the optimal prefilter, and derive simple formulas for the operator norm approximation error. This error shows a dramatic dependence on how the postfilter noninteger shift is chosen. We explain the meaning of this shift in practical applications, describe how to choose it, and plot optimally shifted prefilter approximation errors for 95 different Daubechies, Symlet, and B-spline wavelets. Whereas the truncated inverse is overall superior, the Neumann filters are by far the easiest ones to compute, and for some short support wavelets, they also give the smallest approximation error. For example, for Daubechies 1-5 wavelets, the simplest Neumann prefilter provide an approximation error reduction corresponding to 100-10 000 times oversampling in a nonprefiltered system.     

Fully automated reduction of ocular artifacts in high-dimensional neural data

The reduction of artifacts in neural data is a key element in improving analysis of brain recordings and the development of effective brain-computer interfaces. This complex problem becomes even more difficult as the number of channels in the neural recording is increased. Here, new techniques based on wavelet thresholding and independent component analysis (ICA) are developed for use in high-dimensional neural data. The wavelet technique uses a discrete wavelet transform with a Haar basis function to localize artifacts in both time and frequency before removing them with thresholding. Wavelet decomposition level is automatically selected based on the smoothness of artifactual wavelet approximation coefficients. The ICA method separates the signal into independent components, detects artifactual components by measuring the offset between the mean and median of each component, and then removing the correct number of components based on the aforementioned offset and the power of the reconstructed signal. A quantitative method for evaluating these techniques is also presented. Through this evaluation, the novel adaptation of wavelet thresholding is shown to produce superior reduction of ocular artifacts when compared to regression, principal component analysis, and ICA.     

Efficient design of orthonormal wavelet bases for signal representation

The efficient representation of a signal as a linear combination of elementary "atoms" or building blocks is central to much signal processing theory and many applications. Wavelets provide a powerful, flexible, and efficiently implementable class of such atoms. In this paper, we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized. Since the squared error is not an explicit function of the design parameters, some form of approximation of this objective is required if conventional optimization techniques are to be used. Previous approximations have resulted in nonconvex optimization problems, which require delicate management of local minima. In this paper, we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved. Constraints on the smoothness of the wavelet can be efficiently incorporated into the design. We show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows. In our examples, we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods.     

Enhanced localized computerized tomography employing the discrete wavelet transform

A new localized computerized tomography technique based on the multiresolution analysis (MRA) implementation of the discrete wavelet transform is proposed. Our technique is based upon viewing the projection data as a set of one-dimensional functions of the space variablet and decomposing each one into an approximation signal and a set of detail signals using MRA. The approximation signal and detiil signals associated with each projection are filtered using the ramp filter || of the standard reconstruction technique filtered back projection to generate the set of filtered projections. It is shown that only a very sparse set of projection data outside of the region of interest (ROI) is required to reconstruct a high-quality image of the ROI and a reasonable image outside of the ROI. Simulation results using the Shepp-Logan head phantom are presented to demonstrate the proposed technique.