2 . have summarized the process from continuous wavelet transform to r wavelet transform to gradually eliminate redundancy , the method of constructing biorthogonal and compactly supported wavelets , function ' s decomposition based on orthogonal or biorthogonal basis , the time - frequency characterization of the first generation wavelet transform and the application of the multi - resolution characterization in image compression ( 2 )评述了从连续小波变换到r小波变换的去冗余过程、紧支撑双正交小波的构造、基于第一代小波的函数正交分解( mallat算法)与双正交分解(推广的mallat算法) 、小波变换的时频分析特性及多分辨分析特性在图像压缩中的应用。
We study the design of haar wavelet for scale = a ( a2 ) and present a decomposition and reconstruction algorithm in chapter 3 . secondly , in chapter 4 we study the design of orthonormal mutiwavelets of multiplicity r with scale = a ( a2 ) . by the factorization theory , we give parametric expressions for orthonormal causal fir multifilter banks of r = 2 and scale = 4 , and we found the length of scaling function can be controlled by the parameters . finally , we provide the error analysis between discrete multiwavelet transform coefficients and continue multiwavelet transform coefficients 由于多小波变换系数的计算是直接与其预滤波方式相联系的，而在单小波变换系数计算中之所以能由近似表示就是因为尺度函数具有低通特性和平移正交性，由此我们研究了能满足以上要求的预滤波，并对离散小波变换系数和连续小波变换系数之间的差异作了分析，从误差分析结果我们可以预见：为了减少误差我们可以通过对预滤波的进一步设计来控制。
By means of the x - y scheme and three - dimensional of the cwt , finding the significant difference between the heroin addicts and the healthy persons under some scales and between some time - interval . a primary criterion was obtained , upon which the 15 heroin addicts were identified and 3 healthy persons were misjudged 通过连续小波变换的二维及三维立体图，发现在一定尺度下和一定时间段内，海洛因吸毒者与正常人脉象信号的连续小波变换有显著差异，并给出了初步的判据，依此判据， 15例吸毒者全被检测出来，而正常人z01 、 z10和z15被误判为吸毒者。
At the same time , the optimum detector of ffd and tsd in wavelet domain have been investigated according to properties of cwt . they are wavelet - domain - segmented - replica - correlator ( wdsrc ) and wavelet - domain - replica - correlation - integration ( wdrci ) . and we have proved that their performances are consistent with those in time domain 同时又依据连续小波变换的性质推导出ffd和tsd信道小波变换域的最佳检测器：小波域的分段副本相关器( wdsrc )和小波域的副本相关积分器( wdrci ) ，并从理论和仿真证明了它们与相应的时域检测器性能的一致性，优于小波域的副本相关器( wdrc ) 。
These years wavelet theory has been widely applied in underwater signal processing . whereas its excellent time - frequency localization , this dissertation takes continuous wavelet transform ( cwt ) as research tool and devoted to systematic research and deep exploration of two aspects in underwater signal processing field - estimation of parameters and target classification and identification 近年来小波分析在水下信号处理方面的应用得到了长足的发展，鉴于其良好的时频局部化特点，本文将基于连续小波变换的时频分析作为工具，就参数估计和目标识别两方面的问题做了系统研究和深入探讨。
The effectiveness of this method is confirmed by simulated data and experimental data . moreover , the faults on the outer ring , inner ring and rolling element can be recognized by the time - delayed correlation demodulation . moreover , the time - frequency analysis methods , wigner - ville distribution and wavelet transform , are studied in this paper 结果表明：连续小波变换( cwt )可以诊断齿轮局部故障，但是其计算耗时，不宜用于实时诊断；离散小波变换( dwt )可以诊断滚动轴承故障，且可分辨轴承内环故障、外环故障及滚珠故障。
