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1、外文翻译（原文）-1-WAVELET DE-NOISING BY MEANS OF TRIMMED THRESHOLDINGAbstract:Wavelet thresholding de-noising techniques provide a new way to reduce noise in signal. However, the soft thresholding is best in reducing noise but worst in preservingedges, and hard thresholding is best in preserving edges but
2、worst in de-noising. Motivated by finding a more general case that incorporates the soft and hard thresholding to achieve a compromise between the two methods, the trimmed thresholding method is proposed in this paper. Finally, the experiment results and the power spectral analysis show that the tri
3、mmed thresholding is superior to hard and soft thresholding methods.I. INTRODUCTIONDe-noising is a permanent topic for engineers and applied scientists. In recent years, wavelet de-noising has been more and more extensive in signal processing. As a new signal processing method,wavelet analysis has c
4、haracteristics of multi-resolution and multi-scale.It can make us observe the signal progressively from coarse to fine and have the ability to perform local signal characteristics in both time domain and frequency domain. Wavelet transform de-noising is an important aspect to make wavelet analysis a
5、pplied in engineering practice. In principle, any arithmetic that can use the Fourier transform can use wavelet transform,and it is not limited by short-time window.So it is widely used in signal processing. There are many ways of wavelet de-noising, the more influential, and most commonly used two
6、methods are wavelet transform modulus maxima method of noise reduction and nonlinear wavelet threshold de-noising method. In signal processing, noise reduction with a small crossing analysis has been more widely used, It has been successfully applied in many fields. Such as the seismic signal noise
7、reduction, remote sensing image noise reduction, speech signal noise reduction, noise reduction of nonlinear time series. II. PRINCIPLE OF WAVELET MULTIRESOLUTION-2-Wavelet de-noising is based on the multiresolution analysis. S.Malla gave a method of wavelet decomposition according to the principle
8、of multiresolution.Given a scaling function , its translates and dilates () generate subspace ,such that. （1）There exists a wavelet , it translates and dilates produce a basis of the detail subspace to give .So we can get.，And a signal x(n) can be decomposed by （2） （3）Where are the discrete detail c
9、oefficients of the signal at level and are the approximation coefficients at level , and are low-pass filter and high-pass filter respectively corresponding to some wavelet basis and they are connected by （4） Where N is the length of the filters.The algorithm of the reconstruct of the signal is （5）
10、will be gotten, which is the original signal , when repeating the reconstruct formula （5）.III. DE-NOISING BY WAVELET THRESHOLDINGThe method of wavelet threshold de-noising is based on the principle of the 外文翻译（原文）multiresolution analysis. The discrete detail coefficients and the discrete approximati
11、on coefficients can be obtained by a multi-level wavelet decompose 2. A noisy one-dimensional signal model can be expressed as follows: Among them, is the signal with noise. is the useful signal, is the noise signal. Here we consider as a Gaussian white noise of level 1.It is usually a high-frequenc
12、y signal. But in engineering practice is usually a low-frequency signal, or some stable signal. Therefore, we can use the following method of de-noising: First use wavelet decomposition to the signal (see in Figure 1), obtained by the wavelet decomposition layer is a part of the signal of series of
13、large-scale approximation and the details section. In Figure 1 CA3 is called the approximation signal or the smoothing signal, it is corresponded to the low frequency signal.CD1, CD2, CD3 are called the detail signal. They are corresponded to the signal frequency components, the noise part is usuall
14、y included in the CDI, CD2, CD3. Therefore, we can process the wavelet coefficients with threshold form and then reconstruct the signal to remove the noise. The purpose of removing noise from is to suppress the noise part of the signal to recover the true signal from .Figure 1 Three wavelet decompos
15、itionWavelet decomposition transforms signal from time-domain to time-scale domain, and it can describe the local feature well in both time domain and frequency domain. Because the amplitude of the discrete detail coefficients of the noise decreases with the level increasing, we can select a threshold, modify and process all of the discrete detail coefficients at all scale by threshold method so as to remove noise. The de-noising procedure proceeds in three steps:(1) Decomposition(2) Threshold detail coefficients(3) Reconstruction.
