外文翻譯---信號噪聲消除和離散小波變換

1、<p>　　Eliminate Signal Noise With Discrete Wavelet Transformation</p><p>　　The wavelet transform is a mathematical tool that's becoming quite useful for analyzing many types of signals. It has been

2、proven especially useful in data compression, as well as in adaptive equalizer and transmultiplexer applications.</p><p>　　信號噪聲消除和離散小波變換</p><p>　　小波變換是一種在分析成為許多類型的信號很有用的數(shù)學(xué)工具。它已被證明在數(shù)據(jù)壓縮以及自適應(yīng)均衡器和t

3、ransmultiplexer應(yīng)用中有特別的用途。</p><p>　　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

4、 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

5、for signal and image reconstruction.</p><p>　　小波是一種具有特定的形狀與有限的時間的波。有幾個家庭,或連結(jié)相似類型的小波,沿用至今。幾名去元唯一存在的哈爾積、雙正交。在每一個這樣的家庭小波具有共同的特性。例如,家庭展品雙正交小波變換的線性相位一種</p><p>　　Wavelet analysis is simply the process

6、 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 in

7、to 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 fu

8、ndamental operation.</p><p>　　小波分析是分解信號轉(zhuǎn)變成移位和規(guī)?；姹镜囊粋€特定的小波的簡單過程。小波分析的一個重要的基本性質(zhì)是在重建的過程中重新完美的組裝腐爛的信號或形象變成原始形式而不丟失信息。因?yàn)橐驗(yàn)樗m用于三個具體的應(yīng)用，通過檢測小波理論,我們發(fā)現(xiàn)它具有非常大的作用,例如依靠他們進(jìn)行重建的基本操作。</p><p>　　There are no se

9、t 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 th

10、is reason, it's 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 explora

11、tion of wavelet concepts convenient.</p><p>　　小波分析中母小波的選擇是沒有設(shè)定規(guī)則的。母小波性能的選擇取決于進(jìn)行檢測的信號的性能和分析的要求。因?yàn)檫@個原因,它是讓你輕松探索和試驗(yàn)以許多不同的小波和輸入信號中合適的工具。以下的例子使用MATLAB仿真,小波工具箱,使得勘探和Simulink對小波的概念更加方便。</p><p>　　In thi

12、s 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.</p>

13、<p>　　在這篇文章中,我們使用小波為例(叫做母體小波)是小波積，db4.名字中的四代表濾波的序號，與8序列相對應(yīng)。</p><p>　　The Discrete Wavelet Transform (DWT) is commonly employed using dyadic multirate filter banks, which are sets of filters that divid

14、e 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 f

15、ilters, then the outputs of the low-pass filter are the approximation coefficients. Also, the outputs of the high-pass filter are the detail coeffici</p><p>　　離散小波變換(DWT)通常被應(yīng)用于多頻濾波器采集的配對,將過濾信號頻帶劃分成subbands方面

16、。這些濾波器是由低通、高通、帶通濾波器組成的。如果是小波濾波器濾波器是由低通、高通濾波器的特殊小波濾波器,然后低通濾波器的輸出的近似系數(shù)。同時,這個輸出也是高通濾波器細(xì)節(jié)系數(shù)。</p><p>　　The process of obtaining the approximation and detail coefficients is called decomposition. Termed multilevel

17、 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.

18、</p><p>　　近似數(shù)和細(xì)節(jié)系數(shù)獲得的過程稱為分解。可以重復(fù),與歷屆近似(低通濾波器的輸出第一銀行)依次被分解,這樣一個信號分解為許多組件的過程被稱為多級分解。</p><p>　　A two-level decomposition is shown in Figure 1. In this illustration, a2 represents the approximation

19、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 am

20、ount of data present.</p><p>　　二級分解如圖1所示。在上圖中,a2代表近似系數(shù),而d1 d2代表了二級分解所造成的細(xì)節(jié)系數(shù)。每個分解后,我們使用二級分解把任何其他樣品,因此,減少數(shù)據(jù)量的百分比。</p><p>　　The Inverse Discrete Wavelet Transform (IDWT) reconstructs a signal from

21、 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 inserti

22、on of zeros between samples in a signal. The right side of the figure shows an example of reconstruction.</p><p>　　通過分解逆離散小波變換得到一個信號重構(gòu)的細(xì)節(jié)系數(shù)近。IDWT不同于在upsampling和過濾的DWT的順序。Upsampling,也稱為插值，是指在零嵌入樣本之間的一個信號。右邊的圖

23、顯示了一例重建。</p><p>　　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 fi

24、lter 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 rep

25、resented by the reconstruction.</p><p>　　另一種解釋是,分析數(shù)字濾波器在左邊降低銀行利率的輸入信號和輸出信號產(chǎn)生多個不同的利率。銀行的分析濾波器組進(jìn)行小波分解。綜合濾波器對增加的銀行利率輸入信號生成一個單一的輸出信號。重組了它所代表的數(shù)據(jù)。</p><p>　　The Filters Are The Key</p><p>

26、　　過濾器是其中最為關(guān)鍵的因素</p><p>　　Now one might ask, what's unique about wavelet filter banks? The magic is in the filters themselves. By choosing filters that are intimately related for both decomposition and re

27、construction processes, the effects of aliasing, which can be introduced by the decimation, are removed.</p><p>　　現(xiàn)在你可能會問,什么是小波濾波器的獨(dú)特之處?神奇的是過濾器本身。</p><p>　　通過選擇分解與重構(gòu)過程中密切相關(guān)的過濾器，那些導(dǎo)致死機(jī)的混疊影響被消除了&l

28、t;/p><p>　　When the signal is reconstructed, it doesn't exhibit any aliasing or distortion (right side of Fig. 1). As a result, the output is said to be a perfect reconstruction. </p><p>　　當(dāng)信號重

29、建,它不展示任何或扭曲走樣(右邊的圖1)。作為一個結(jié)果,產(chǎn)量被認(rèn)為是一個完美的重建。</p><p>　　Wavelet filters have finite length. They aren't truncated versions of infinitely long filter re-sponses. Because of this property, wavelet filter banks

30、 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

31、to these kinds of signals with excellent results. This is due to their ability to locate short-time (local) high-frequency featur</p><p>　　小波濾波器長度有限。他們不是截?cái)嗟陌姹緍e-sponses無窮長過濾。因?yàn)檫@個性質(zhì)、小波濾波器可以執(zhí)行局部的分析或考試局部區(qū)域的一個稍大

32、的信號。局部分析作為一個值得考慮的信號處理方式是有間斷。小波變換可以很好的應(yīng)用到這些類型的信號。這是由于他們有能力在同一時間內(nèi)來定位短時(局部)信號的高頻特征和解決低頻行為。</p><p>　　As stated earlier, perfect reconstruction is an important property of wavelet filter banks. When the analysis

33、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

34、 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.</p><p>　　如前所述,完全重構(gòu)是小波濾波器的一個重要的性質(zhì)。當(dāng)銀行的分

35、析濾波器組輸出連接到合成濾波器輸入和適當(dāng)?shù)难舆t銀行使用一致,如圖1,然后整個系統(tǒng)的輸出是相同的輸入。如果一個閾值,并將其應(yīng)用到輸出操作的DWT和小波系數(shù)低于指定的值的移除,那么系統(tǒng)將會做一個“去噪”功能。</p><p>　　Two different threshold operations can be viewed in Figure 2. In the first, hard thresholding,

36、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. <

37、/p><p>　　兩個不同的閾值操作可以從圖2看出來。首先,硬閾值,其絕對值系數(shù)低于閾值設(shè)置為零。硬閾值是延長第二技術(shù)。軟閾值,通過減少剩余的非零系數(shù)進(jìn)行對零操作。</p><p>　　Furthermore, to compare the output signal with the input, additional delays are introduced into the input

38、 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. </p><p&g

39、t;　　此外,比較輸出信號的輸入,額外延遲引入輸入信號路徑。數(shù)據(jù)序列是一個務(wù)實(shí)的一個重要方面,實(shí)時實(shí)現(xiàn)。輸入、輸出、殘差信號顯示在圖6個能被顯示在圖7范圍。</p><p>　　The wavelet transmultiplexer (WTM) provides an interesting example of the perfect reconstruction property of the DWT. T

40、he 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. </p>

41、<p>　　小波transmultiplexer(WTM)提供了一個完全重構(gòu)的財(cái)產(chǎn)DWT的有趣例子。結(jié)合兩個源信號的transmultiplexer傳輸一個鏈接,然后將兩路信號的接收終端渠道(圖8),輸入被認(rèn)為是基帶信號。</p><p>　　The ability of wavelets to provide perfect reconstruction of independent signals

42、, 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

43、to demonstrate the absence of signal corruption.</p><p>　　小波分析的能力不僅僅是提供完美重建獨(dú)立的信號,傳送一個單一的通信鏈路,表現(xiàn)在圖9。通道1和2完美再現(xiàn),如上的綜合誤差的情節(jié)。錯誤痕跡繪制大圖像上,這證明沒有垂直的信號錯誤。</p><p>　　The model shown in Figure 8 demonstrates

44、 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.</p><p>　　該模

45、型顯示在圖8演示了一個通道transmultiplexer。但是這個方法可以擴(kuò)展到一個任意數(shù)量的渠道。注意,總數(shù)據(jù)率仍限于奈奎斯特率的高速數(shù)據(jù)連接</p><p>　　Similarities With FDM Operation</p><p>　　FDM操作上的相同點(diǎn)</p><p>　　The operation of a WTM is analogous

46、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 re

47、ceiving end, the transmitted signal is filtered to separate the two adjacent frequency channels. The signals are then demodulated back to baseband.</p><p>　　WTM的操作在幾個方面與多路復(fù)用器(FDM)域相類似。在一個FDM、基帶信號濾波和調(diào)制到鄰近頻帶,總

48、結(jié)在一起,然后發(fā)送到一個單一的鏈接。在接收端,信號傳輸過濾分離的兩個相鄰的頻率通道。然后解調(diào)信號回到基帶。</p><p>　　The filters need to pass the desired signal through the filter passband with as little distortion as possible. In addition, the filters must str

49、ongly 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 const

50、raints generally require longer and more expensive filters. </p><p>　　過濾器必須通過過濾通頻帶使得期望信號失真盡可能少。此外,強(qiáng)衰減過濾器必須給相鄰信號提供一個強(qiáng)力的過渡濾波器的阻帶通頻帶。這個過程限制從一個頻帶到下一個頻帶的一定量的干擾,或者信號泄漏。這些限制通常需要更長和更昂貴的過濾器。</p><p>　　Oft

51、en, 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 ban

52、dwidth for each input signal.</p><p>　　通常,將通過一名未分頻帶稱為一個防御系統(tǒng),兩者之間的調(diào)制頻帶對FDM過濾器放寬要求。這減少頻譜效率,從而減少每一個輸入信號的可用帶寬。</p><p>　　In a WTM, the filtering performed by the synthesis and analysis wavelet filter

53、s 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, exhi

54、biting slow transitions from passband to stopband, and providing significant distortion in their response. </p><p>　　在一個WTM,過濾由合成和分析小波濾波器的濾波相似的步伐帶。并且,得帶相當(dāng)于頻率調(diào)制的插值。從頻域角度出發(fā), 他們的反應(yīng)，對小波濾波器較差譜過濾器,展示的轉(zhuǎn)折,慢阻帶通頻帶,提供重

55、要的改進(jìn)。</p><p>　　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 th

56、e input signals and, thus, perfect extraction of the multiplexed inputs.</p><p>　　分析和綜合濾波器濾波在一起完全消除和信號混疊失真使WTM特別。生產(chǎn)完全重構(gòu)輸入信號,從而完善的提取多路復(fù)用的投入。</p><p>　　Ideal spectral efficiency can be achieved wit

57、h 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 communicat

58、ions 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 i

59、nterference is </p><p>　　理想的光譜效率可能達(dá)到與WTM相。實(shí)施方面的限制通道濾鏡使得帶外信號的滲入和扭曲。在傳統(tǒng)的差分方法中,每一個頻道在同樣的通訊系統(tǒng)需要自身濾波,并易于混淆與鄰近的渠道。但是WTM方法對整個通信信道只需要一個單一的帶通濾波器,channel-to-channel將干擾消除。</p><p>　　Keep in mind that a nois

60、y 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.</p><p>　　記住一

61、個復(fù)雜的輸入信號可以導(dǎo)致不完美的重建輸入信號。此外, 在WTM-based對熔融沉積體系。信道噪聲的影響和其他的損傷的恢復(fù)信號可以是不同的。</p><p>　　Image compression is becoming increasingly important as the efficient use of available transmission bandwidth becomes more comp

62、lex. 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 s

63、uch that it's still possible to achieve a reasonable reconstruction of the image. Wavelet transforms have this capability.</p><p>　　圖像壓縮越來越重要的有效傳輸帶寬可用就變得更為復(fù)雜了。作為復(fù)雜性的增加,必須優(yōu)化系統(tǒng)資源使用最小帶寬和記憶。一種方法就是利用這些資源優(yōu)化圖像壓

64、縮。這種方法，還是有可能以達(dá)到一個合理的重建圖像。小波變換具有這能力。</p><p>　　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 coeffici

65、ents. 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. </p><p>　　壓縮過程類似于早

66、些時候用過的一個去噪的例子。唯一的區(qū)別在于閾值應(yīng)用于細(xì)節(jié)系數(shù)。兩個ap-proaches可在小波工具箱的細(xì)節(jié)系數(shù)閾值時的二維數(shù)據(jù)壓縮。這些都是全球性的閾值和水平閾值。</p><p>　　In this example, we allow the Wavelet Toolbox to derive a global threshold for our example image. The image shown

67、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 bi

68、orthogonal spline wavelet bior3.7, which specifies a third-order reconstruction filter and a seventh-order decomposition filter.</p><p>　　在這個例子中,我們讓小波工具箱來獲得一個全球的底線即我們的目標(biāo)圖像。圖像顯示在圖10分解利用二維離散小波分析工具(類似于一維工具發(fā)現(xiàn)圖3)

69、。這個例子,我們決定執(zhí)行一個二級分解利用雙正交樣條小波函數(shù)的bior3.7,指定一個線性濾波器和seventh-order分解重構(gòu)濾波器。</p><p>　　The compression tools available in the Wavelet Toolbox perform only the thresholding portion of the compression process. Its per

70、formance 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 fac

71、tors.</p><p>　　壓縮工具可在小波工具箱完成只是閾值壓縮的過程的一部分。在小波其性能測量剩余的非零元素的百分比。當(dāng)實(shí)現(xiàn)了一個實(shí)際的壓縮方案,你需要進(jìn)一步考慮因素的量化和bit-allocation . .</p><p>　　The two-dimensional wavelet compression tool automatically generates a thres

72、hold 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 th

73、an 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 User's Guide for more information on how these percentages were calcul&l

74、t;/p><p>　　Wavelet analysis is a new and promising tool which complements traditional signal processing techniques. It can offer significant advantages for real-time systems, and it opens the door to new and ex

75、citing communications applications.</p><p>　　For Further Information:</p><p>　　C. Taswell, "The What, How, and Why of Wavelet Shrinkage Denoising," Computing In Science And Engineering

76、, vol. 2, no. 3, May/June 2000, p. 12-19. </p><p>　　Department of Applied Science Wavelet Group, Lawrence Livermore National Laboratory, www.llnl.gov/das/wavelet/wavelet.html. </p><p>　　G. Cheru

77、bini; J. Cioffi; E. Eleftheriou; S. Olcer; "Filter Bank Modulation Techniques for Very High-Speed Digital Subscriber Lines," IEEE Communications Magazine, vol. 38, no. 5, May 2000, p. 98-104. </p><p&

78、gt;　　G. Strang and T. Nguyen, Wavelets And Filter Banks, Wellesley-Cambridge Press, 1997. </p><p>　　M. Misiti; Y. Misiti; G. Oppenheim; J.M. Poggi, Wavelet Toolbox User's Guide, The MathWorks Inc., 1996.

79、 </p><p>　　二維小波壓縮工具自動生成一個閾值選擇閾值方法的基礎(chǔ)上(圖10,再)。我們選擇“清除接近0”,設(shè)置這個全球門檻4。當(dāng)我們點(diǎn)擊壓縮按鈕,所有的價(jià)值系數(shù)小于4(在這個例子中,49.81%的人)還必須為零。盡管這種情況下,98.98%的原始圖像能量被保留。在小波工具箱用戶指南有更多的信息關(guān)于這些百分比計(jì)算公式。</p><p>　　小波分析是一種有潛力的新工具,與傳統(tǒng)的信號

80、處理技術(shù)相輔相成。它能提供為實(shí)時系統(tǒng)明顯的優(yōu)勢,它會打開到新的和令人興奮的通訊應(yīng)用的門。</p><p>　　1。Taswell >,“The What, How, and Why of Wavelet Shrinkage Denoising,第二卷,第3次,2000年5 / 6月,p。12-19。</p><p>　　2。應(yīng)用科學(xué)部門的小波基,勞倫斯利佛摩國家實(shí)驗(yàn)室,www.lln

81、l.gov /這個/小波/ wavelet.html。</p><p>　　3。Cherubini >,《Cioffi;大腸Eleftheriou,s . Olcer;“過濾銀行調(diào)制技術(shù)非常高速數(shù)字電話線”,臺灣通訊雜志,中國土木水利工程學(xué)刊,38歲,沒有。5、2000年5月,p。98 - 104。</p><p>　　4 G. Strang and T. Nguyen,小波濾波器,