基本介紹
coiflet小波性質,套用,係數,Matlab程式,雙正交Coiflet小波,定義,性質,
coiflet小波性質
定義
一個正交小波（orthogonal wavelet）系統若符合以下條件，則稱為Generalized Coiflet Wavelet(GOC)。
其中
為小波函式，
為調整函式
濾波器長度與消失動量
若
為濾波器長度，而
為系統消失動量，則最小的
為：
近線性相位（Near-linear phase）濾波器
其中
，
則為常數項。因此
具有漸進線性相位（asymptotic linear phase）的特性：
套用
Coiflet小波除了被使用在影像壓縮外，當前也有被使用在電力系統訊號監測上。
係數
下表為coiflet小波調整函式C6~30的係數，小波函式的係數可以藉由每兩個係數變換一次符號來推導(例如C6 wavelet = {−0.022140543057, 0.102859456942, 0.544281086116, −1.205718913884, 0.477859456942, 0.102859456942})
| k | C6 | C12 | C18 | C24 | C30 |
|---|---|---|---|---|---|
-10 | -0.0002999290456692 | ||||
-9 | 0.0005071055047161 | ||||
-8 | 0.0012619224228619 | 0.0030805734519904 | |||
-7 | -0.0023044502875399 | -0.0058821563280714 | |||
-6 | -0.0053648373418441 | -0.0103890503269406 | -0.0143282246988201 | ||
-5 | 0.0110062534156628 | 0.0227249229665297 | 0.0331043666129858 | ||
-4 | 0.0231751934774337 | 0.0331671209583407 | 0.0377344771391261 | 0.0398380343959686 | |
-3 | -0.0586402759669371 | -0.0930155289574539 | -0.1149284838038540 | -0.1299967565094460 | |
-2 | -0.1028594569415370 | -0.0952791806220162 | -0.0864415271204239 | -0.0793053059248983 | -0.0736051069489375 |
-1 | 0.4778594569415370 | 0.5460420930695330 | 0.5730066705472950 | 0.5873348100322010 | 0.5961918029174380 |
0 | 1.2057189138830700 | 1.1493647877137300 | 1.1225705137406600 | 1.1062529100791000 | 1.0950165427080700 |
1 | 0.5442810861169260 | 0.5897343873912380 | 0.6059671435456480 | 0.6143146193357710 | 0.6194005181568410 |
2 | -0.1028594569415370 | -0.1081712141834230 | -0.1015402815097780 | -0.0942254750477914 | -0.0877346296564723 |
3 | -0.0221405430584631 | -0.0840529609215432 | -0.1163925015231710 | -0.1360762293560410 | -0.1492888402656790 |
4 | 0.0334888203265590 | 0.0488681886423339 | 0.0556272739169390 | 0.0583893855505615 | |
5 | 0.0079357672259240 | 0.0224584819240757 | 0.0354716628454062 | 0.0462091445541337 | |
6 | -0.0025784067122813 | -0.0127392020220977 | -0.0215126323101745 | -0.0279425853727641 | |
7 | -0.0010190107982153 | -0.0036409178311325 | -0.0080020216899011 | -0.0129534995030117 | |
8 | 0.0015804102019152 | 0.0053053298270610 | 0.0095622335982613 | ||
9 | 0.0006593303475864 | 0.0017911878553906 | 0.0034387669687710 | ||
10 | -0.0001003855491065 | -0.0008330003901883 | -0.0023498958688271 | ||
11 | -0.0000489314685106 | -0.0003676592334273 | -0.0009016444801393 | ||
12 | 0.0000881604532320 | 0.0004268915950172 | |||
13 | 0.0000441656938246 | 0.0001984938227975 | |||
14 | -0.0000046098383254 | -0.0000582936877724 | |||
15 | -0.0000025243583600 | -0.0000300806359640 | |||
16 | 0.0000052336193200 | ||||
17 | 0.0000029150058427 | ||||
18 | -0.0000002296399300 | ||||
19 | -0.0000001358212135 |
Matlab程式
F = coifwavf(W)會回傳N=str2num(W)的coiflet小波的調整函式，其中N只能為1~5的整數。
雙正交Coiflet小波
定義
一個order為
的雙正交Coiflet小波需符合以下條件：
