信号噪声消除和离散小波变换外文翻译.docx

eliminate signal noise with discrete wavelet transformationthe 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 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 original 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 the 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 corresponds 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-pass, 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 repeated, 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 figure 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。the inverse discrete wavelet transform (idwt) reconstructs a signal from the approximation and detail coefficients derived from decomposition. the idwt differs from the dwt in that it requires upsampling and filtering, in that order. upsampling, also known as interpolating, means the insertion of zeros between samples in a signal. the right side of the figure shows an example of reconstruction.通过分解逆离散小波变换得到一个信号重构的细节系数近。idwt不同于在upsampling和过滤的dwt的顺序。upsampling,也称为插值，是指在零嵌入样本之间的一个信号。右边的图显示了一例重建。another way to interpret the figure is that the analysis filter bank on the left reduces the rate of an input signal and produces multiple output signals with varying rates. the analysis filter bank performs the dwt represented by the decomposition. the synthesis filter bank on the right increases the rates of multiple input signals while combining them into a single output signal. it performs the idwt represented by the reconstruction.另一种解释是,分析数字滤波器在左边降低银行利率的输入信号和输出信号产生多个不同的利率。银行的分析滤波器组进行小波分解。综合滤波器对增加的银行利率输入信号生成一个单一的输出信号。重组了它所代表的数据。the filters are the key过滤器是其中最为关键的因素now one might ask, whats unique about wavelet filter banks? the magic is in the filters themselves. by choosing filters that are intimately related for both decomposition and reconstruction processes, the effects of aliasing, which can be introduced by the decimation, are removed.现在你可能会问,什么是小波滤波器的独特之处?神奇的是过滤器本身。通过选择分解与重构过程中密切相关的过滤器，那些导致死机的混叠影响被消除了when the signal is reconstructed, it doesnt exhibit any aliasing or distortion (right side of fig. 1). as a result, the output is said to be a perfect reconstruction. 当信号重建,它不展示任何或扭曲走样(右边的图1)。作为一个结果,产量被认为是一个完美的重建。wavelet filters have finite length. they arent truncated versions of infinitely long filter re-sponses. because of this property, wavelet filter banks can perform local analysis, or the examination of a localized area of a larger signal. local analysis is an important consideration when dealing with signals that have discontinuities. wavelet transforms can be applied to these kinds of signals with excellent results. this is due to their ability to locate short-time (local) high-frequency features of a signal and resolve low-frequency behavior at the same time. 小波滤波器长度有限。他们不是截断的版本re-sponses无穷长过滤。因为这个性质、小波滤波器可以执行局部的分析或考试局部区域的一个稍大的信号。局部分析作为一个值得考虑的信号处理方式是有间断。小波变换可以很好的应用到这些类型的信号。这是由于他们有能力在同一时间内来定位短时(局部)信号的高频特征和解决低频行为。as stated earlier, perfect reconstruction is an important property of wavelet filter banks. when the analysis filter bank output is connected to the synthesis filter bank input and the proper delays for alignment are used, as in figure 1, then the output of the entire system is identical to the input. if a threshold operation is applied to the output of the dwt and wavelet coefficients that are below a specified value are removed, then the system will perform a de-noising function.如前所述,完全重构是小波滤波器的一个重要的性质。当银行的分析滤波器组输出连接到合成滤波器输入和适当的延迟银行使用一致,如图1,然后整个系统的输出是相同的输入。如果一个阈值,并将其应用到输出操作的dwt和小波系数低于指定的值的移除,那么系统将会做一个“去噪”功能。two different threshold operations can be viewed in figure 2. in the first, hard thresholding, coefficients whose absolute values are lower than the threshold are set to zero. hard thresholding is extended by the second technique, soft thresholding, by shrinking the remaining nonzero coefficients toward zero. 两个不同的阈值操作可以从图2看出来。首先,硬阈值,其绝对值系数低于阈值设置为零。硬阈值是延长第二技术。软阈值,通过减少剩余的非零系数进行对零操作。furthermore, to compare the output signal with the input, additional delays are introduced into the input signal path. data alignment is a significant aspect of a practical, real-time implementation. the input, output, and residual signals shown in figure 6 can be viewed in the scope display in figure 7. 此外,比较输出信号的输入,额外延迟引入输入信号路径。数据序列是一个务实的一个重要方面,实时实现。输入、输出、残差信号显示在图6个能被显示在图7范围。the wavelet transmultiplexer (wtm) provides an interesting example of the perfect reconstruction property of the dwt. the transmultiplexer combines two source signals for transmission over a single link, then separates the two signals at the receiving end of the channel (fig. 8). the inputs are assumed to be baseband signals. 小波transmultiplexer(wtm)提供了一个完全重构的财产dwt的有趣例子。结合两个源信号的transmultiplexer传输一个链接,然后将两路信号的接收终端渠道(图8),输入被认为是基带信号。the ability of wavelets to provide perfect reconstruction of independent signals, transmitted over a single communications link, is demonstrated in figure 9. channels 1 and 2 are perfectly recreated, as indicated by the combined error plot. the error trace is plotted with an expanded vertical scale to demonstrate the absence of signal corruption.小波分析的能力不仅仅是提供完美重建独立的信号,传送一个单一的通信链路,表现在图9。通道1和2完美再现,如上的综合误差的情节。错误痕迹绘制大图像上,这证明没有垂直的信号错误。the model shown in figure 8 demonstrates a two-channel transmultiplexer. but the method can be extended to an arbitrary number of channels. note that the total data rate is still limited by the nyquist rate of the high-speed data link.该模型显示在图8演示了一个通道transmultiplexer。但是这个方法可以扩展到一个任意数量的渠道。注意,总数据率仍限于奈奎斯特率的高速数据连接similarities with fdm operationfdm操作上的相同点the operation of a wtm is analogous to a frequency-domain multiplexer (fdm) in several respects. in an fdm, baseband input signals are filtered and modulated into adjacent frequency bands, summed together, and then transmitted over a single link. on the receiving end, the transmitted signal is filtered to separate the two adjacent frequency channels. the signals are then demodulated back to baseband.wtm的操作在几个方面与多路复用器(fdm)域相类似。在一个fdm、基带信号滤波和调制到邻近频带,总结在一起,然后发送到一个单一的链接。在接收端,信号传输过滤分离的两个相邻的频率通道。然后解调信号回到基带。the filters need to pass the desired signal through the filter passband with as little distortion as possible. in addition, the filters must strongly attenuate the adjacent signal to provide a sharp transition from the filter passband to its stopband. this process limits the amount of crosstalk, or signal leakage, from one frequency band to the next. these constraints generally require longer and more expensive filters. 过滤器必须通过过滤通频带使得期望信号失真尽可能少。此外,强衰减过滤器必须给相邻信号提供一个强力的过渡滤波器的阻带通频带。这个过程限制从一个频带到下一个频带的一定量的干扰,或者信号泄漏。这些限制通常需要更长和更昂贵的过滤器。often, fdm employs an unused frequency band, known as a guard band, between the two modulated frequency bands to relax the requirements on the fdm filters. this decreases spectral efficiency, thereby reducing the usable bandwidth for each input signal.通常,将通过一名未分频带称为一个防御系统,两者之间的调制频带对fdm过滤器放宽要求。这减少频谱效率,从而减少每一个输入信号的可用带宽。in a wtm, the filtering performed by the synthesis and analysis wavelet filters is analogous to the filtering steps in the fdm. plus, the interpolation in the idwt is equivalent to frequency modulation. from a frequency-domain perspective, the wavelet filters are fairly poor spectral filters, exhibiting slow transitions from passband to stopband, and providing significant distortion in their response. 在一个wtm,过滤由合成和分析小波滤波器的滤波相似的步伐带。并且,得带相当于频率调制的插值。从频域角度出发, 他们的反应，对小波滤波器较差谱过滤器,展示的转折,慢阻带通频带,提供重要的改进。what makes the wtm special, though, is that the analysis and synthesis filters together completely cancel the filter distortions and signal aliasing. that produces perfect reconstruction of the input signals and, thus, perfect extraction of the multiplexed inputs.分析和综合滤波器滤波在一起完全消除和信号混叠失真使wtm特别。生产完全重构输入信号,从而完善的提取多路复用的投入。ideal spectral efficiency can be achieved with the wtm, because no guard band is required. practical limitations of implementing the channel filter create out-of-band leakage and distortion. in the conventional fdm approach, every channel within the same communications system requires its own filter and is susceptible to crosstalk from neighboring channels. but the wtm method only requires a single bandpass filter for the entire communications channel, and the channel-to-channel interference is eliminated. 理想的光谱效率可能达到与wtm相。实施方面的限制通道滤镜使得带外信号的渗入和扭曲。在传统的差分方法中,每一个频道在同样的通讯系统需要自身滤波,并易于混淆与邻近的渠道。但是wtm方法对整个通信信道只需要一个单一的带通滤波器,channel-to-channel将干扰消除。keep in mind that a noisy link can cause imperfect reconstruction of the input signals. furthermore, the effects of channel noise and other impairments on the recovered signals can differ in fdm- and wtm-based systems.记住一个复杂的输入信号可以导致不完美的重建输入信号。此外, 在wtm-based对熔融沉积体系。信道噪声的影响和其他的损伤的恢复信号可以是不同的。image compression is becoming increasingly important as the efficient use of available transmission bandwidth becomes more complex. as complexity increases, system resources must be optimized to use minimal bandwidth and memory. one way to optimize these resources is to employ image compression. the method and amount of compression needs to be such that its still possible to achieve a reasonable reconstruction of the image. wavelet transforms have this capability.图像压缩越来越重要的有效传输带宽可用就变得更为复杂了。作为复杂性的增加,必须优化系统资源使用最小带宽和记忆。一种方法就是利用这些资源优化图像压缩。这种方法，还是有可能以达到一个合理的重建图像。小波变换具有这能力。the compression procedure is similar to that of de-noising used in an earlier example. the only difference lies in the thresholding applied to the detail coefficients. two ap-proaches are available in the wavelet toolbox for thresholding detail coefficients when compressing two-dimensional data. these are global thresholding and level thresholding. 压缩过程类似于早些时候用过的一个去噪的例子。唯一的区别在于阈值应用于细节系数。两个ap-proaches可在小波工具箱的细节系数阈值时的二维数据压缩。这些都是全球性的阈值和水平阈值。in this example, we allow the wavelet toolbox to derive a global threshold for our example image. the image shown in figure 10 was decomposed using the two-dimensional discrete wavelet analysis tool (similar to the one-dimensional tool found in figure 3). for this example, we decided to perform a two-level decomposition using the biorthogonal spline wavelet bior3.7, which specifies a third-order reconstruction filter and a seventh-order decomposition filter.在这个例子中,我们让小波工具箱来获得一个全球的底线即我们的目标图像。图像显示在图10分解利用二维离散小波分析工具(类似于一维工具发现图3)。这个例子,我们决定执行一个二级分解利用双正交样条小波函数的bior3.7,指定一个线性滤波器和seventh-order分解重构滤波器。the compression tools available in the wavelet toolbox perform only the thresholding portion of the compression process. its performance is measured by the percentage of remaining nonzero elements in the wavelet decomposition. when implementing a real-world compression scheme, one would need to further consider quantization and bit-allocation factors.压缩工具可在小波工具箱完成只是阈值压缩的过程的一部分。在小波其性能测量剩余的非零元素的百分比。当实现了一个实际的压缩方案,你需要进一步考虑因素的量化和bit-allocation . .the two-dimensional wavelet compression tool automatically generates a threshold based on the thresholding method selected (fig. 10, again). we picked remove near 0, which sets this global threshold to 4. when we click on the compress button, all coefficients whose values are less than 4 (in this case, 49.81%) are forced to zero. in spite of this case, 98.98% of the original image energy is retained. see the wavelet toolbox users guide fo