时间尺度的多分辨率综合

本文根据小波分析的基本原理,对原子钟信号进行多分辨分解,将分解后的小波变换系数进行加权平均,得到不同小波尺度综合原子时的加权平均小波变换系数,然后由小波变换的重构条件,反演综合时间尺度,由于对原子钟信号进行小波分解,利用不同尺度的小波变换系数的小波方差进行加权平均,这样既要考虑不同原子钟在稳定性方面的差异,又顾及同一台原子在钟在不同小波尺度的变化特性,最后根据陕西天文台国家授时中心的实测数据对这种     

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。     

A variational method for designing adaptive bandlimited wavelets

This paper proposes a new method of estimating an orthogonal bounded spectrum wavelet from a given signal. The method is based on minimizing the distance of the wavelet and the given signal in the sense of the metric of the L ² space. In this method, the amplitude and phase of the mother wavelet are optimized simultaneously. The Lagrange multipliers technique is applied to consider the constraints due to the bounded spectrum wavelet and orthogonality conditions. The variational method reduced the optimal matching problem to the solution of a set of functional equations for the amplitude and phase of the optimal-matched bandlimited wavelet spectrum. Continuous functional equations are written with respect to Fourier coefficients of phase of transfer function of the quadrate low-pass filter at the sampled frequencies, and asset of discrete algebraic equations allows us to design the wavelet directly from the signal of interest. To demonstrate the performance of the presented method in this paper, it is employed to determine the matched wavelets of some specified signals.     

一种基于子波变换的信号滤噪改进方法

对子波变换多尺度下信号与噪声的不同性质进行了研究,提出了一种在子波域不同尺度上选取不同的滤噪方法,该方法将经典的软阈值滤噪与子波变换的模极值传播特性在一定尺度上有机结合起来处理信号.在改善信噪比的同时,也尽可能地保持原信号的边缘信息和精细特征.通过仿真验证了该方法的实用性和优越性.     

一种优化的频率驾驭算法研究

为满足各应用领域对高精度时间性能不断提升的需求,该文设计实现了一种迭代的优化频率驾驭算法,主要分为纸面时间计算和实际物理信号实现两个部分。其中纸面时间计算采用ALGOS算法,利用实时原子钟数据和Circular T公报数据计算获得准确可靠的时间尺度,保障了驾驭参考的准确性和实时性。实时物理信号实现采用最优二次型高斯控制算法与Kalman算法综合,通过实时调整参数,计算出最优的频率驾驭量,将该驾驭量输送至频率调整设备,最终实现高精度时间信号的输出,整个驾驭系统是闭环的。该文基于我国时间基准保持系统和原子钟组,搭建试验平台,采用该算法对一台氢钟进行为期140天的频率驾驭,最终对输出的物理信号进行性能评估。试验结果表明,该算法有效提高了驾驭后物理信号的准确度和稳定度,驾驭后信号与国际标准时间协调世界时(UTC)相比,相位偏差保持在±3 ns以内,且30天稳定度优于5×10–16。     

基于小波变换的音频信号基频提取

通过对小波变换表征信号突变原理的研究，给出了基于小波变换的音频信号基频提取的原理和算法。在算法的实现过程中，利用信号在时域和频域的对应关系提出了一种动态确定小波变换最佳尺度的方法，克服了固定变换尺度在检测基频变化范围大的声音信号时的不足，并将数学统计方法引入到极大值点的提取。在音频信号的实时基频检测实验中，该算法较准确地定位最佳尺度和极大值点，取得了较好的基频提取结果。     

一种优化的频率驾驭算法研究

为满足各应用领域对高精度时间性能不断提升的需求,该文设计实现了一种迭代的优化频率驾驭算法,主要分为纸面时间计算和实际物理信号实现两个部分。其中纸面时间计算采用ALGOS算法,利用实时原子钟数据和Circular T公报数据计算获得准确可靠的时间尺度,保障了驾驭参考的准确性和实时性。实时物理信号实现采用最优二次型高斯控制算法与Kalman算法综合,通过实时调整参数,计算出最优的频率驾驭量,将该驾驭量输送至频率调整设备,最终实现高精度时间信号的输出,整个驾驭系统是闭环的。该文基于我国时间基准保持系统和原子钟组,搭建试验平台,采用该算法对一台氢钟进行为期140天的频率驾驭,最终对输出的物理信号进行性能评估。试验结果表明,该算法有效提高了驾驭后物理信号的准确度和稳定度,驾驭后信号与国际标准时间协调世界时(UTC)相比,相位偏差保持在±3 ns以内,且30天稳定度优于5×10^–16。     

由小波变换的模极大值快速重构信号

本文从多尺度分析的思想出发，提出一种由信号小波变换的模极大值快速重构信号的方法，在不同尺度上，以阶跃函数在该尺度上的小波变换作为基函数，利用模极大值拟合信号的小波变换，然后进行小波反演得到重构信号。这种快速算法具有明确而直观的物理意义，实现简单方便。文中还给出了对重构信号的误差修正方法，数值方法的结果表明，这种快速重构算法对不同类型的信号同样有效。     

A translation- and scale-invariant adaptive wavelet transform

This paper presents a new approach to deal with the translation- and scale-invariant problem of the discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonormal wavelet, we adaptively renormalized a signal. The renormalized signal is then decomposed by using the algorithm of the conventional DWT. The final wavelet transform coefficients, called adaptive wavelet invariant moments (AWIM), are proved to be both translation- and scale-invariant. Furthermore, as an application, we define a new textural feature in the framework of our adaptive wavelet decomposition, show its stability to shift and scaling, and demonstrate its efficiency for the task of scale-invariant texture identification.     

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.     

Wavelets and differential-dilation equations

It is shown how differential-dilation equations can be constructed using iterations, similar to the iterations with which wavelets and dilation equations are constructed. A continuous-time wavelet is constructed starting from a differential-dilation equation. It has compact support and excellent time domain and frequency domain localization properties. The wavelet is infinitely differentiable and therefore cannot be obtained using digital filter banks. In addition, the wavelet has excellent approximation properties. New sampling and differentiation techniques are also introduced. Results on image interpolation using the solution of the differential-dilation equation are presented. Examples are given, demonstrating the suitability of the new wavelet function for signal analysis     

基于小波域的电路信号分析

本文在离散小波变换矩阵表示的基础上,由时域方程直接推导了电阻、电感、电容、变压器等电路元件在小波域的等效电路方程,并将之应用于电路分析中.该方法具有推导简单,且能分析电路时-频特征的特点,较单独的时域或频域分析更适合于暂态和瞬变信号的分析.     

应用卫星电视秒信号传播时延值对同步卫星运动周期的子波分析

讨论了子波变换用于信号突变的检测原理，并用这种方法分析了武昌时辰站１９９４年测量由卫星电视传播并由中央电视台发出的秒信号的时间延迟值，精确检出了该信号的突变点，并由此求出了同步卫星运动周期的变化特征。结果表明：利用子波变换能很好揭示同步卫星的运动特性。     

Speed estimation in wireless systems using wavelets

A new technique is described for estimating the speed of a mobile station in a wireless system. The mobile speed maps the characteristic spatial scale of the received signal into a characteristic temporal scale. The continuous wavelet transform tracks changes in the temporal scale to estimate the mobile speed as a function of time. This technique requires neither knowledge of the average received power of the nonstationary signal nor adaptation of a temporal observation window, in contrast to other speed estimators given in the literature. Simulations show the tracking of a variable speed profile     

气缸压力的时频分析及其在内燃机故障诊断中的应用

对气缸压力进行时-频分析,探讨了气缸压力信号与气阀机构状态之间的关系.对气缸压力信号进行二进小波分解,计算分解后尺度1上信号各频带的能量比,从中提取诊断特征量,从而对气阀机构进行故障诊断.结果表明此方法是可行、有效的.     

基于自适应阈值函数的小波阈值去噪方法

去噪是小波分析的一个重要应用领域,相对于其它方法,小波变换具有对信号时频局部性详细刻画的优势。在信号的去噪处理过程中,如何在削弱噪声的同时又最大限度的保留信号的奇异性特征是信号去噪研究的一个核心问题。该文提出一种基于自适应阈值函数的小波去噪方法,通过调整阈值函数实现在信号小波分解的细尺度上去除噪声的同时又尽量保留信号细节系数,而在宽尺度上最大限度地滤除噪声部分的小波系数。通过对blocks, bumps和水下目标回波信号的仿真实验证明,该方法和现有的阈值去噪方法相比,具有显著的优势,能够在滤除噪声的同时很好地保留信号的奇异性特征。     

间歇混沌合成1/f噪声的相关特性分析

本文利用非线性随机微分方程来合成间歇混沌信号,针对该信号表现出的1/f噪声特征,在不同消失矩的小波基下进行相关特性分析.仿真结果发现,在功率谱的中间频段内,该信号的功率谱密度表现出典型的1/f噪声特性,其小波变换系数方差与相应的小波尺度呈对数线性关系;且在该频段内,部分尺度下该间歇性信号的小波变换系数的相关性随小波基的消失矩的增大而减小,在另一部分尺度下该相关性则随着消失矩的增大而增大.实验结果表明,随小波消失矩的增大,并非在所有尺度下小波变换对该间歇性信号均具有去相关作用.论文讨论了小波变换系数的方差和尺度的关系,详细分析了小波变换系数的相关性随小波消失矩的变化趋势.     

高温合金中微小缺陷超声检测信号的小波去噪研究

本文首先建立了高温合金材料微小缺陷的超声检测信号模型,然后在分析仪器电噪声、晶粒散射噪声、缺陷信号的频谱分布及小波变换特性的基础上,采用一种用一个尺度间变化的门限阈值来去除噪声的小波变换系数再重构检测信号的方法提高信噪比。计算机仿真分析和实验结果表明,该方法不仅具有很好的去噪效果,而且重构的缺陷回波的波形失真度小,有利于进一步作定量检测。     

一种基于小波分解的直扩信号检测方法

针对直接序列扩频（DSSS）信号检测的问题,提出了一种对接收信号时域自相关进行小波分解的方法。该方法对于进行了载波调制的直扩信号,其所在频带未知时无法设计前置滤渡器,从而造成检测性能下降的情况,给出了一种可行的解决方案。计算机模拟表明,在该情况下,本方法具有较好的检测性能。     

Discrete inverses for nonorthogonal wavelet transforms

Discrete nonorthogonal wavelet transforms play an important role in signal processing by offering finer resolution in time and scale than their orthogonal counterparts. The standard inversion procedure for such transforms is a finite expansion in terms of the analyzing wavelet. While this approximation works quite well for many signals, it fails to achieve good accuracy or requires an excessive number of scales for others. This paper proposes several algorithms that provide more adequate inversion and compares them in the case of Morlet wavelets. In the process, both practical and theoretical issues for the inversion of nonorthogonal wavelet transforms are discussed