外文翻译--小波分析在信号处理中的应用.(2)

MATLAB是Math Works公司开发的一种跨平台的，用于矩阵数值计算的简单高效的数学语言，与其它计算机高级语言如C, C++, Fortran, Basic, Pascal等相比，MATLAB语言编程要简洁得多，编程语句更加接近数学描述，可读性好，其强大的圆形功能和可视化数据处理能力也是其他高级语言望尘莫及的。

四 综述

众所周知，由于图像在采集、数字化和传输过程中常受到各种噪声的干扰，从而使数字图像中包含了大量的噪声。能否从受扰信号中获得去噪的信息，不仅与干扰的性质和信号形式有关，也与信号的处理方式有关。在实际应用中，针对不同性质的信号和干扰，寻找最佳的处理方法降低噪声，一直是信号处理领域广泛讨论的重要问题。

小波包分析的应用是与小波包分析的理论研究紧密地结合在一起的。现在，它已经在科技信息产业领域取得了令人瞩目的成就。如今，信号处理已经成为当代科学技术工作的重要组成部分，信号处理的目的就是：准确的分析、诊断、编码、压缩和量化、快速传递或存储、精确的恢复（或重构）。从数学的角度来看，信号与图像处理可以统一看作是信号处理，在小波包分析的许多分析的许多应用中，都可以归结为信号处理问题。

小波包分析的应用领域十分广泛，它包括：信号分析、图象处理、量子力学、理论物理、军事电子对抗与武器的智能化、计算机分类与识别、音乐与语言的人工合成、医学成像与诊断、地震勘探数据处理、大型机械的故障诊断等方面。例如，在数学方面，它已用于数值分析、构造快速数值方法、曲线曲面构造、微分方程求解、控制论等。在信号分析方面的滤波、去噪、压缩、传递等。

在图像处理方面的图象压缩、分类、识别与诊断，去污等。在医学成像方面的减少B超、CT、核磁共振成像的时间，提高分辨率等。小波包分析用于信号与图像压缩是小波包分析应用的一个重要方面。它的特点是压缩比高，压缩速度快，压缩后能保持信号与图像的特征不变，且在传递中可以抗干扰。基于小波包分析的压缩方法很多，比较成功的有小波包最好基方法，小波域纹理模型方法，小波变换零树压缩，小波变换向量压缩等。小波包在信号分析中的应用也十分广泛。它可以用于边界的处理与滤波、时频分析、信噪分离与提取弱信号、求分形指数、信号的识别与诊断以及多尺度边缘检测等。

A ·The wavelet study the meaning and background

In practical applications, the different nature of the signal and interference, to find the best processing method to reduce noise, the important issue is widely discussed in the field of signal processing. Currently, there are many methods can be used to signal noise reduction, such as median filtering, low pass filtering, Fourier transform, etc., but they are filtered out by the useful part of the signal details. The traditional signal de-noising method smooth signal only from the time domain or frequency domain are given the results of the statistical average. Time domain or frequency domain characteristics of the effective signal to noise removal, but not taking into account the local and the whole picture of the signal in the time domain and frequency domain. More Practice has proved that the classical approach based on the Fourier transform of the filter, and can not be non-stationary signal analysis and processing, denoising effect can not meet the requirements of engineering application development. In recent years, many papers non-stationary signal wavelet threshold de-noising method. Donoho and Johnstone contaminated with Gaussian noise signal de-noising by thresholding wavelet coefficients. Commonly used hard threshold rule and soft threshold rule set to filter out the noise from the signal high-frequency wavelet coefficients to zero. Practice has proved that these wavelet thresholding method with approximate optimization features, has a good performance in the field of non-stationary signals. The threshold rule mainly depends on the choice of parameters. For example, the hard threshold and soft threshold depends on the choice of a single parameter - global

threshold lambda lambda adjustment is critical However, due to the non-linearity of the wavelet transform. Threshold is too small or too large, will be directly related to the pros and cons of the signal de-noising effect. When the threshold value is dependent on a number of parameters, the problem will become more complex. In fact, the effective threshold denoising method is often determined based on wavelet

decomposition at different levels depending on the threshold parameter, and then determine the appropriate threshold rule. Compared with the wavelet analysis, wavelet packet analysis (Wavelet Packet Analysis) to provide a more detailed analysis for the signal, it will band division of multi-level, multi-resolution analysis is no breakdown of the high-frequency part of the further decomposition, and according to the characteristic of the signal being analyzed, adaptive selection of the corresponding frequency band, to match with the signal spectrum, thereby increasing the time - frequency resolution. The wavelet packet transform is the promotion of the wavelet transform in signal with more flexibility than the wavelet transform. Using wavelet packet transform to the signal decomposition, the low-frequency part and high-frequency components are further decomposed. Wavelet packet signal de-noising threshold method combined with good application value.

At present, both in engineering applications and theoretical study, removal of signal interference noise is a hot topic. Extract valid signal is band a wide interference or white noise pollution signal mixed with noise signal, has been an important part of signal processing. The traditional digital signal analysis and processing is to establish the basis of Fourier transform, Fourier transform stationary signals in the time domain and frequency domain algorithm to convert each other, but can not accurately represent the signal time-frequency localization properties. For non-stationary signals people use short-time Fourier transform, but it uses a fixed short-time window function is a single-resolution signal analysis method, there are some irreparable defect. Wavelet theory is developed on the basis of Fourier transform and short-time Fourier transform, and it has the characteristics of multi-resolution analysis, have the ability to characterize the local signal characteristics in the time domain and frequency domain, is an excellent tool for signal analysis . Wavelet transform (Wavelet transform) emerged in the mid 1980s when the frequency domain signal analysis tools, since 1989 S.Mallat the first time since the introduction of wavelet transform image processing, wavelet transform its excellent time-frequency local capacity and good to go related capacity in the field of image compression coding has been widely used, and achieved good results. Multi-resolution wavelet transform, time-frequency localization characteristics and calculation speed and other attributes, which makes the wavelet transform has been widely applied in the field of geophysics. Such as: using

wavelet transform gravity and magnetic parameters of the extraction, the magnitude of the error of the reconstructed signal with the original signal after the wavelet analysis as a standard to select the wavelet basis

Seismic data denoising. As technology advances, the wavelet packet analysis (Wavelet Packet Analysis) method developed wavelet packet analysis is the expansion of the wavelet analysis, with a very wide range of application. It is able to signal to provide a more detailed analysis of the method, it is the band multi-level framing is not broken down at high frequency portion of the discrete wavelet transform is further analyzed, and according to the characteristics of the signal to be analyzed, adaptively selecting the frequency band corresponding to , with the signal matching, thereby increasing the time-frequency resolution. The wavelet packet analysis (wavelet packet analysis) signal to be able to provide a more detailed analysis of the method, it is divided band multi-level wavelet analysis no breakdown of the high frequency portion is further decomposed, and according to the characteristic of the signal being analyzed, adaptively select the appropriate frequency band, the signal spectrum to match, thus wavelet packet has a wider range of applications. Fractal theory of wavelet packet by U.S. scientists BBMandelbrot in the mid-1970s the creation of \describe the complexity of the signal, it is mainly research, widely used in many fields of science, including the recent wavelet analysis and fractal theory, is used to determine the overlap complex chemical signals in the group scores and the peak position and fractal characteristics of the DNA sequence. Using wavelet packet analysis for signal noise reduction, an intuitive and effective wavelet packet de-noising method is the direct thresholding wavelet packet decomposition coefficients, select the filter factor coefficient signal reconstruction preserved, and ultimately to drop The purpose of the noise. Signal de-noising using wavelet packet analysis, feature extraction and recognition is an important application of wavelet packet analysis in digital signal processing.

B·The development and application of wavelet analysis Wavelet packet analysis of the application of theoretical research and wavelet packet analysis closely together. Now, it has been made in the field of science and technology information industry made remarkable achievements. Electronic information technology is an area of six high-tech focus, image and signal processing. Today, the signal processing has become an important part of the contemporary scientific and technical work, the purpose of signal processing: an accurate analysis, diagnosis, compression coding

and quantization, rapid transfer or storage, accurately restore (or reconstructed). From the point of view of mathematically, signal and image processing can be unified as a signal processing, wavelet packet analysis many many applications of the analysis, can be attributed to the signal processing problem. Now, for its nature with practice is stable and unchanging signal processing ideal tool still Fourier analysis. However, in practical applications, the vast majority of the signal is stable, while the tool is especially suitable for non-stationary signal is wavelet packet analysis.

In recent years, the combined fund research projects and corporate research projects. China in the application of wavelet packet analysis carried out some exploration.

First, wavelet packet signal analysis, the the boundary singularity processing method and wavelet packet processing in the frequency domain positioning is perfect from the application point of view. Harmonic wavelet packet analysis method, and the harmonic wavelet packet and fractal combined to solve practical problems in engineering.

Secondly, in the operation of the rotor vibration signal detection of the fault feature analysis simulation and practical research. Motor noise analysis method using wavelet packet analysis theory to identify the impact threshold to noise singular signal of the acceleration of the vehicle, using the method of wavelet packet analysis and come to a satisfactory conclusion, while the harmonic wavelet packet combined with the fractal theory. Automobile gearbox nonlinear crack fault feature, the first application of the method of combining wavelet analysis and fractal theory and the technical design of the vehicle driveline. Middle and low agricultural transport light goods vehicle driveline job stability is not good, the problem of short working life, in the practical application of engineering to explore a new way.

Next, using theoretical analysis, experiments and software implementation phase junction station, namely the use of wavelet packet analysis and computer programs to achieve the digital signal processing. In the analysis of non-stationary signals, respectively, using existing technology and wavelet packet analysis method, the fractal method is used, expect improvements in digital signal processing. To reflect the complex characteristics of the information to improve the accuracy of the signal analysis and detection, reached the advanced level. On the basis of cooperation with others to complete a set of signal processing methods and techniques of high-speed data processing system.

In recent years, the range of applications of the wavelet packet is increasingly far and wide. Wavelet packet analysis any signal can be mapped to a basic wavelet telescopic pan from the wavelet function up. Signal to achieve a reasonable separation of the different frequency bands at different times, without losing any of

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