1、Eliminate Signal Noise With Discrete Wavelet Transformation The wavelet transform is a mathematical tool thats becoming quite useful for analyzing many types of signals. It has been proven especially useful in data compression, as well as in adaptive equalizer and transmultiplexer applications. 信号噪声
2、消除和离散小波变换 小波变换是一种 在 分析成为许多类型的信号很有用的数学工具。它已被证明 在 数据压缩以及自适应均衡器和 transmultiplexer 应用 中有特别的用途 。 A wavelet is a small, localized wave of a particular shape and finite duration. Several families, or collections of similar types of wavelets, are in use today. A few go by the names of Haar, Daubechies, and
3、Biorthogonal. Wavelets within each of these families share common properties. For instance, the Biorthogonal wavelet family exhibits linear phase, which is an important characteristic for signal and image reconstruction. 小波是一种 具有 特定的形状与有限的时间 的波 。 有几个家庭 ,或连结相似类型的小波 ,沿用至今。几名去元唯一存在的哈尔积、双正交。在每一个这样的家庭小波具
4、有共同的特性。例如 ,家庭展品双正交小波变换的线性相位一种 Wavelet analysis is simply the process of decomposing a signal into shifted and scaled versions of a particular wavelet. An important property of wavelet analysis is perfect reconstruction, which is the process of reassembling a decomposed signal or image into its origi
5、nal form without loss of information. By examining wavelet theory as it applies to three specific applications, we find that it works so well because these examples rely on perfect reconstruction for their fundamental operation. 小波分析是分解信号转变成移 位和规模化版本的一个特定的小波 的 简单过程。小波分析的一个重要的基本性质是 在 重建的过程中重新 完美的组装腐烂
6、的信号或形象 变成 原始形式而不丢失信息。因为因为它适用于三个具体的应用 ， 通过检测小波理论 ,我们发现它 具有非常大的作用 ,例如依靠他们进行重建 的基本操作。 There are no set rules for the choice of the mother wavelet used in wavelet analysis. The choice depends on the properties of the mother wavelet, the properties of the signal to be examined, and the requirements of th
7、e analysis. For this reason, its convenient to have tools that let you easily explore and experiment with many different wavelets and input signals. The following examples use MATLAB, the Wavelet Toolbox, and Simulink to make exploration of wavelet concepts convenient. 小波分析 中母小波的选择是没有设定规则的。母小波 性能 的选
8、择取决于进行检测的 信号 的性能和 分析的要求。因为这个原因 ,它是让你轻松探索和试验以许多不同的小波和输入信号 中合适的工具 。以下的例子使用MATLAB 仿真 ,小波工具箱 ,使 得 勘探和 Simulink 对小波的概念 更加 方便 。 In this article, the wavelet we use as an example (called the mother wavelet) is the Daubechies wavelet, db4. The 4 in the name represents the order of the filter, which correspo
9、nds to eight coefficients. 在这篇文章中 ,我们使用小波为例 (叫做母体小波 )是小波积， db4.名字中的四代表滤波的序号，与 8 序列相对应。 The Discrete Wavelet Transform (DWT) is commonly employed using dyadic multirate filter banks, which are sets of filters that divide a signal frequency band into subbands. These filter banks are comprised of low-p
10、ass, high-pass, or bandpass filters. If the filter banks are wavelet filter banks that consist of special low-pass and high-pass wavelet filters, then the outputs of the low-pass filter are the approximation coefficients. Also, the outputs of the high-pass filter are the detail coefficients. . 离散小波变
11、换 (DWT)通常 被应用于 多频滤波器 采集的 配对 ,将 过滤信号频带划分成 subbands 方面 。这些滤波 器是由 低通、高通、带通滤波器 组成的 。如果是小波滤波器滤波器是由低通、高通滤波器的特殊小波滤波器 ,然后低通滤波器的输出的近似系数。同时 ,这个输出也是 高通滤波器细节系数 。 The process of obtaining the approximation and detail coefficients is called decomposition. Termed multilevel decomposition, this process can be repea
12、ted, with successive approximations (the output of the low-pass filter in the first bank) being decomposed in turn, so that one signal is broken down into a number of components. 近似数 和细节系数获得的过程 称为 分解。可以重复 ,与历届近似 (低通滤波器的输出第一银行 )依次被分解 ,这样一个信号分解为许多组件 的过程被称为多级分解。 A two-level decomposition is shown in Fi
13、gure 1. In this illustration, a2 represents the approximation coefficients, while d2 and d1 represent the detail coefficients resulting from the two-level decomposition. After each decomposition, we employ decimation by two to remove every other sample and, therefore, reduce the amount of data present. 二级分解如图 1 所示。在上图中 ,a2 代表近似系数 ,而 d1 d2 代表了二级分解所造成的细节 系数。每个分解后 ,我们使用 二级分解 把任何其他 样品 ,因此 ,减少数据量的 百分比 。
