查看“︁Symlet”︁的源代码

Symlet 小波是比利時女性物理暨數學家[[英格丽·多贝西|英格麗·多貝西]]（Ingrid Daubechies）所提出的一種{{Link-en|正交小波|Orthogonal_wavelet}}（orthogonal wavelet），Symlet的波形比多貝西小波更對稱，最大值會在波形中心。

== 性質 ==

* 定義<ref>{{Cite book|chapter=Ten Lectures on Wavelets|url=http://epubs.siam.org/doi/book/10.1137/1.9781611970104|publisher=Society for Industrial and Applied Mathematics|date=1992-01|isbn=978-0-89871-274-2|doi=10.1137/1.9781611970104.ch8|language=en|first=Ingrid|last=Daubechies|access-date=2023-01-05|archive-date=2023-01-05|archive-url=https://web.archive.org/web/20230105175327/https://epubs.siam.org/doi/book/10.1137/1.9781611970104|dead-url=no}}</ref>
* 濾波器長度與消失動量

相同長度的 Symlet 和[[多貝西小波]]有相同的[[消失動量]]。2p-point Symlet 的消失動量是 p。

== 應用 ==
symlet 可以應用在馬達的能量錯位偵測和特徵提取<ref>{{Cite journal |last=Saputra |first=P. P. S. |last2=Misbah |last3=Eliyani |last4=Firmansyah |first4=R. |last5=Lastomo |first5=D. |date=2019-07 |title=Haar and Symlet Discrete Wavelete Transform for Identification Misalignment on Three Phase Induction Motor Using Energy Level and Feature Extraction |url=https://dx.doi.org/10.1088/1742-6596/1179/1/012093 |journal=Journal of Physics: Conference Series |language=en |volume=1179 |issue=1 |doi=10.1088/1742-6596/1179/1/012093 |issn=1742-6596}}</ref>，以及去除聲音中的高斯雜訊<ref>{{Cite journal |last=Chavan |first=Dr. Mahesh S. |last2=Chavan |first2=Mrs Manjusha N. |last3=Gaikwad |first3=Dr. M.S. |date=2010-06-10 |title=Studies on Implementation of Wavelet for denoising Speech Signal |url=http://dx.doi.org/10.5120/711-1001 |journal=International Journal of Computer Applications |volume=3 |issue=2 |doi=10.5120/711-1001 |issn=0975-8887}}</ref>。

== 濾波器 ==
以下列出 4,6,8,10 點 symlet 作為濾波器的係數。其中g是低頻的濾波器，h是高頻的濾波器。<ref>{{Cite web|title=Symlets 2 wavelet (sym2) properties, filters and functions - Wavelet Properties Browser|url=https://wavelets.pybytes.com/wavelet/sym2/|access-date=2023-01-05|website=wavelets.pybytes.com|archive-date=2023-01-05|archive-url=https://web.archive.org/web/20230105172939/https://wavelets.pybytes.com/wavelet/sym2/|dead-url=no}}</ref>

{| class="wikitable"
|+Symlet 濾波器係數
!n
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
|-
!<math>g_{4}</math>
| -0.1294
| 0.2241
| 0.8365
|0.4829
|
|
|
|
|
|
|-
!<math>h_{4}</math>
| -0.4829
| 0.8365
| -0.2241
| -0.1294
|
|
|
|
|
|
|-
!<math>g_{6}</math>
|0.0352
| -0.0854
| -0.1350
|0.4598
| 0.8068
| 0.3326
|
|
|
|
|-
!<math>h_{4}</math>
| -0.3326
|0.8068
| -0.4598
| -0.1350
|0.0854
|0.0352
|
|
|
|
|-
!<math>g_{8}</math>
| -0.0757
| -0.0296
|0.4976
|0.8037
|0.2978
| -0.0992
| -0.0126
|0.0322
|
|
|-
!<math>h_{8}</math>
| -0.0322
| -0.0126
|0.0992
|0.2978
| -0.8037
|0.49761
|0.0296
| -0.0757
|
|
|-
!<math>g_{10}</math>
|0.0273
|0.0295
| -0.0391
|0.1993
|0.7234
|0.6339
|0.0166
| -0.1753
| -0.0211
|0.0195
|-
!<math>h_{10}</math>
| -0.0195
| -0.0211
|0.1753
|0.0166
| -0.6339
|0.7234
| -0.1993
| -0.0391
| -0.0295
|
|}

== Matlab 程式 ==
f = symwavf(wname) 會回傳 N=str2num(W) 的 symlet 小波的調整函式。<ref>{{Cite web|title=Symlet wavelet filter - MATLAB symwavf|url=https://www.mathworks.com/help/wavelet/ref/symwavf.html|access-date=2023-01-05|website=www.mathworks.com|archive-date=2023-01-05|archive-url=https://web.archive.org/web/20230105172940/https://www.mathworks.com/help/wavelet/ref/symwavf.html|dead-url=no}}</ref>

== 參考資料 ==
{{Reflist}}