《小波函数及matlab常用指令》由会员分享，可在线阅读，更多相关《小波函数及matlab常用指令（119页珍藏版）》请在金锄头文库上搜索。
1、常用小波函数及Matlab常用指令 一 、常用小波函数与标准傅立叶变换相比，小波分析中用到的 小波函数没有唯一性，小波函数 具有多样 性。由此而带来的问题是使用不同的小波基分 析同一个问题会产生不同的结果，没有一个选 择最优小波基的统一方法。目前主要是通过用 小波分析方法处理信号的结果与理论分析结果 的误差莱判定小波基的好坏，并由此选定小波 基。常用的指导性选择标准有：(1) 的支撑长度。即当时间或频率趋于无穷大时，上述各量从有限值收敛到0的速度；(2) 对称型。它在图象处理中对于避免移相非常有用;(3) (若存在)的消失矩阶数。对于压缩非常有用;(4)正则性。对信号或图象的重构获得较好的平滑
2、效果非常有用。l1、Haar 小波lwaveinfo(haar) lHAARINFO Information on Haar wavelet. l Haar Wavelet l General characteristics: Compactly supported l wavelet, the oldest and the simplest wavelet.l scaling function phi = 1 on 0 1 and 0 otherwise. l wavelet function psi = 1 on 0 0.5, = -1 on 0.5 1 and 0 otherwise.l
3、 Family Haar l Short name haar l Examples haar is the same as db1l Orthogonal yes l Biorthogonal yes l Compact support yes l DWT possible l CWT possiblel Support width 1 l Filters length 2 l Regularity haar is not continuous l Symmetry yes l Number of vanishing moments for psi 1图:在命令窗口输入waveinfo(haa
4、r)lDBINFO Information on Daubechies wavelets. l Daubechies Wavelets l General characteristics: Compactly supported wavelets with extremal phase and highest number of vanishing moments for a given support width. Associated scaling filters are l minimum-phase filters. l Family Daubechies l Short name
5、db l Order N N strictly positive integer l Examples db1 or haar, db4, db152、db系列小波l Orthogonal yesl Biorthogonal yesl Compact support yesl DWT possiblel CWT possiblel Support width 2N-1l Filters length 2Nl Regularity about 0.2 N for large Nl Symmetry far froml Number of vanishing moments for psi N图:
6、l3、Biorthogonal(biorNr.Nd)小波系主要特点体现在具有线性相位型，主要应用于信号和图象的重构中。通常表示为biorNr.Nd形式。Nr=1 Nd=1,3,5; Nr=2 Nd=2,4,6,8Nr=3 Nd=1,3,5,7,9; Nr=4 Nd=4Nr=5 Nd=5; Nr=6 Nd=8lGeneral characteristics: Compactly supported biorthogonal spline wavelets for which symmetry and exact reconstruction are possible with FIR filte
7、rs (in orthogonal case it is impossible except for Haar).l Family Biorthogonal l Short name bior l Order Nr,Nd Nr = 1 , Nd = 1, 3, 5 l r for reconstruction Nr = 2 , Nd = 2, 4, 6, 8 l d for decomposition Nr = 3 , Nd = 1, 3, 5, 7, 9Nr = 4 , Nd = 4Nr = 5 , Nd = 5Nr = 6 , Nd = 8l Examples bior3.1, bior5
8、.5 l Orthogonal（正交） no l Biorthogonal(双正交的) yes l Compact support yes l DWT possible l CWT possible l Support width 2Nr+1 for rec., 2Nd+1 for dec. l Filters length max(2Nr,2Nd)+2 but essentiallyl bior Nr.Nd ld lr effective length effective lengthof Lo_D of Hi_Dl bior 1.1 2 2 l bior 1.3 6 2l bior 1.5
9、 10 2 l bior 2.2 5 3 l bior 2.4 9 3 l bior 2.6 13 3 l bior 2.8 17 3 l bior 3.1 4 4 l bior 3.3 8 4 l bior 3.5 12 4l bior 3.7 16 4l bior 3.9 20 4l bior 4.4 9 7l bior 5.5 9 11l bior 6.8 17 11lRegularity for psi rec. Nr-1 and Nr-2 at the knotslSymmetry yes lNumber of vanishing moments for psi dec. NrlRe
10、mark: bior 4.4 , 5.5 and 6.8 are such that reconstruction and ldecomposition functions and filters are close in value. 图:l4、Coiflet(coifN)小波系由Daubechies构造,N=1,2,3,4,5.具有比dbN更好的对称性。从支撑长度看，具有和db3N及sym3N具有相同的支撑长度，从消失矩的数目看，具有和 db2N和symN相同的消失矩数目。 图:lGeneral characteristics: Compactly supported wavelets with highest number of vanishing moments for both phi and psi for a given support width. l Family Coiflets l Short name coif l Order N N = 1, 2, ., 5 l Examples coif2, coif4 l Orthogonal yes l Biorthogonal yes l Compact support
