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Symlet.cs
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Symlet.cs
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///
/// SharpWave - A refactored port of JWave
/// https://github.com/graetz23/JWave
///
/// MIT License
///
/// Copyright (c) 2020-2024 Christian ([email protected])
///
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
///
/// The above copyright notice and this permission notice shall be included in all
/// copies or substantial portions of the Software.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
/// SOFTWARE.
///
namespace SharpWave
{
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym2/ Thanks!
/// However there are likely to be some rounding errors: ~1e-12.
/// For example: 1.1 => 1,10000000000209 or 3,3 => 3,29999999999917 ..
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
/// TODO Please report the analytical formula for construction, if available
///</remarks>
public class Symlet2 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet2( ) : base( "Symlet 2", 4, 2 ) {
// these coefficients are already orthonormal
_scalingDeCom[ 0 ] = -0.12940952255092145;
_scalingDeCom[ 1 ] = 0.22414386804185735;
_scalingDeCom[ 2 ] = 0.836516303737469;
_scalingDeCom[ 3 ] = 0.48296291314469025;
//
// _waveletDeCom[ 0 ] = -0.48296291314469025;
// _waveletDeCom[ 1 ] = 0.836516303737469;
// _waveletDeCom[ 2 ] = -0.22414386804185735;
// _waveletDeCom[ 3 ] = -0.12940952255092145;
//
// _scalingReCon[ 0 ] = 0.48296291314469025;
// _scalingReCon[ 1 ] = 0.836516303737469;
// _scalingReCon[ 2 ] = 0.22414386804185735;
// _scalingReCon[ 3 ] = -0.12940952255092145;
//
// _waveletReCon[ 0 ] = -0.12940952255092145;
// _waveletReCon[ 1 ] = -0.22414386804185735;
// _waveletReCon[ 2 ] = 0.836516303737469;
// _waveletReCon[ 3 ] = -0.48296291314469025;
//
_buildBaseSystem( ); // build all other from low pass decomposition
} // Symlet2
} // class
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym3/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet3 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet3( ) : base( "Symlet 3", 6, 2) {
_scalingDeCom[ 0 ] = 0.035226291882100656;
_scalingDeCom[ 1 ] = -0.08544127388224149;
_scalingDeCom[ 2 ] = -0.13501102001039084;
_scalingDeCom[ 3 ] = 0.4598775021193313;
_scalingDeCom[ 4 ] = 0.8068915093133388;
_scalingDeCom[ 5 ] = 0.3326705529509569;
_buildBaseSystem( );
} // Symlet3
} // Symlet3
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym4/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet4 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet4( ) : base( "Symlet 4", 8, 2) {
_scalingDeCom[ 0 ] = -0.07576571478927333;
_scalingDeCom[ 1 ] = -0.02963552764599851;
_scalingDeCom[ 2 ] = 0.49761866763201545;
_scalingDeCom[ 3 ] = 0.8037387518059161;
_scalingDeCom[ 4 ] = 0.29785779560527736;
_scalingDeCom[ 5 ] = -0.09921954357684722;
_scalingDeCom[ 6 ] = -0.012603967262037833;
_scalingDeCom[ 7 ] = 0.0322231006040427;
_buildBaseSystem( );
} // Symlet4
} // Symlet4
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym5/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet5 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet5( ) : base( "Symlet 5", 10, 2) {
_scalingDeCom[ 0 ] = 0.027333068345077982;
_scalingDeCom[ 1 ] = 0.029519490925774643;
_scalingDeCom[ 2 ] = -0.039134249302383094;
_scalingDeCom[ 3 ] = 0.1993975339773936;
_scalingDeCom[ 4 ] = 0.7234076904024206;
_scalingDeCom[ 5 ] = 0.6339789634582119;
_scalingDeCom[ 6 ] = 0.01660210576452232;
_scalingDeCom[ 7 ] = -0.17532808990845047;
_scalingDeCom[ 8 ] = -0.021101834024758855;
_scalingDeCom[ 9 ] = 0.019538882735286728;
_buildBaseSystem( );
} // Symlet5
} // Symlet5
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym6/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet6 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet6( ) : base( "Symlet 6", 12, 2) {
_scalingDeCom[ 0 ] = 0.015404109327027373;
_scalingDeCom[ 1 ] = 0.0034907120842174702;
_scalingDeCom[ 2 ] = -0.11799011114819057;
_scalingDeCom[ 3 ] = -0.048311742585633;
_scalingDeCom[ 4 ] = 0.4910559419267466;
_scalingDeCom[ 5 ] = 0.787641141030194;
_scalingDeCom[ 6 ] = 0.3379294217276218;
_scalingDeCom[ 7 ] = -0.07263752278646252;
_scalingDeCom[ 8 ] = -0.021060292512300564;
_scalingDeCom[ 9 ] = 0.04472490177066578;
_scalingDeCom[ 10 ] = 0.0017677118642428036;
_scalingDeCom[ 11 ] = -0.007800708325034148;
_buildBaseSystem( );
} // Symlet6
} // Symlet6
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym7/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet7 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet7( ) : base( "Symlet 7", 14, 2) {
_scalingDeCom[ 0 ] = 0.002681814568257878;
_scalingDeCom[ 1 ] = -0.0010473848886829163;
_scalingDeCom[ 2 ] = -0.01263630340325193;
_scalingDeCom[ 3 ] = 0.03051551316596357;
_scalingDeCom[ 4 ] = 0.0678926935013727;
_scalingDeCom[ 5 ] = -0.049552834937127255;
_scalingDeCom[ 6 ] = 0.017441255086855827;
_scalingDeCom[ 7 ] = 0.5361019170917628;
_scalingDeCom[ 8 ] = 0.767764317003164;
_scalingDeCom[ 9 ] = 0.2886296317515146;
_scalingDeCom[ 10 ] = -0.14004724044296152;
_scalingDeCom[ 11 ] = -0.10780823770381774;
_scalingDeCom[ 12 ] = 0.004010244871533663;
_scalingDeCom[ 13 ] = 0.010268176708511255;
_buildBaseSystem( );
} // Symlet7
} // Symlet7
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym8/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet8 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet8( ) : base( "Symlet 8", 16, 2) {
_scalingDeCom[ 0 ] = -0.0033824159510061256;
_scalingDeCom[ 1 ] = -0.0005421323317911481;
_scalingDeCom[ 2 ] = 0.03169508781149298;
_scalingDeCom[ 3 ] = 0.007607487324917605;
_scalingDeCom[ 4 ] = -0.1432942383508097;
_scalingDeCom[ 5 ] = -0.061273359067658524;
_scalingDeCom[ 6 ] = 0.4813596512583722;
_scalingDeCom[ 7 ] = 0.7771857517005235;
_scalingDeCom[ 8 ] = 0.3644418948353314;
_scalingDeCom[ 9 ] = -0.05194583810770904;
_scalingDeCom[ 10 ] = -0.027219029917056003;
_scalingDeCom[ 11 ] = 0.049137179673607506;
_scalingDeCom[ 12 ] = 0.003808752013890615;
_scalingDeCom[ 13 ] = -0.01495225833704823;
_scalingDeCom[ 14 ] = -0.0003029205147213668;
_scalingDeCom[ 15 ] = 0.0018899503327594609;
_buildBaseSystem( );
} // Symlet8
} // Symlet8
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym9/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet9 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet9( ) : base( "Symlet 9", 18, 2) {
_scalingDeCom[ 0 ] = 0.0014009155259146807;
_scalingDeCom[ 1 ] = 0.0006197808889855868;
_scalingDeCom[ 2 ] = -0.013271967781817119;
_scalingDeCom[ 3 ] = -0.01152821020767923;
_scalingDeCom[ 4 ] = 0.03022487885827568;
_scalingDeCom[ 5 ] = 0.0005834627461258068;
_scalingDeCom[ 6 ] = -0.05456895843083407;
_scalingDeCom[ 7 ] = 0.238760914607303;
_scalingDeCom[ 8 ] = 0.717897082764412;
_scalingDeCom[ 9 ] = 0.6173384491409358;
_scalingDeCom[ 10 ] = 0.035272488035271894;
_scalingDeCom[ 11 ] = -0.19155083129728512;
_scalingDeCom[ 12 ] = -0.018233770779395985;
_scalingDeCom[ 13 ] = 0.06207778930288603;
_scalingDeCom[ 14 ] = 0.008859267493400484;
_scalingDeCom[ 15 ] = -0.010264064027633142;
_scalingDeCom[ 16 ] = -0.0004731544986800831;
_scalingDeCom[ 17 ] = 0.0010694900329086053;
_buildBaseSystem( );
} // Symlet9
} // Symlet9
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym10/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet10 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet10( ) : base( "Symlet 10", 20, 2) {
_scalingDeCom[ 0 ] = 0.0007701598091144901;
_scalingDeCom[ 1 ] = 9.563267072289475e-05;
_scalingDeCom[ 2 ] = -0.008641299277022422;
_scalingDeCom[ 3 ] = -0.0014653825813050513;
_scalingDeCom[ 4 ] = 0.0459272392310922;
_scalingDeCom[ 5 ] = 0.011609893903711381;
_scalingDeCom[ 6 ] = -0.15949427888491757;
_scalingDeCom[ 7 ] = -0.07088053578324385;
_scalingDeCom[ 8 ] = 0.47169066693843925;
_scalingDeCom[ 9 ] = 0.7695100370211071;
_scalingDeCom[ 10 ] = 0.38382676106708546;
_scalingDeCom[ 11 ] = -0.03553674047381755;
_scalingDeCom[ 12 ] = -0.0319900568824278;
_scalingDeCom[ 13 ] = 0.04999497207737669;
_scalingDeCom[ 14 ] = 0.005764912033581909;
_scalingDeCom[ 15 ] = -0.02035493981231129;
_scalingDeCom[ 16 ] = -0.0008043589320165449;
_scalingDeCom[ 17 ] = 0.004593173585311828;
_scalingDeCom[ 18 ] = 5.7036083618494284e-05;
_scalingDeCom[ 19 ] = -0.0004593294210046588;
_buildBaseSystem( );
} // Symlet10
} // Symlet10
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym11/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet11 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet11( ) : base( "Symlet 11", 22, 2) {
_scalingDeCom[ 0 ] = 0.00017172195069934854;
_scalingDeCom[ 1 ] = -3.8795655736158566e-05;
_scalingDeCom[ 2 ] = -0.0017343662672978692;
_scalingDeCom[ 3 ] = 0.0005883527353969915;
_scalingDeCom[ 4 ] = 0.00651249567477145;
_scalingDeCom[ 5 ] = -0.009857934828789794;
_scalingDeCom[ 6 ] = -0.024080841595864003;
_scalingDeCom[ 7 ] = 0.0370374159788594;
_scalingDeCom[ 8 ] = 0.06997679961073414;
_scalingDeCom[ 9 ] = -0.022832651022562687;
_scalingDeCom[ 10 ] = 0.09719839445890947;
_scalingDeCom[ 11 ] = 0.5720229780100871;
_scalingDeCom[ 12 ] = 0.7303435490883957;
_scalingDeCom[ 13 ] = 0.23768990904924897;
_scalingDeCom[ 14 ] = -0.2046547944958006;
_scalingDeCom[ 15 ] = -0.1446023437053156;
_scalingDeCom[ 16 ] = 0.03526675956446655;
_scalingDeCom[ 17 ] = 0.04300019068155228;
_scalingDeCom[ 18 ] = -0.0020034719001093887;
_scalingDeCom[ 19 ] = -0.006389603666454892;
_scalingDeCom[ 20 ] = 0.00011053509764272153;
_scalingDeCom[ 21 ] = 0.0004892636102619239;
_buildBaseSystem( );
} // Symlet11
} // Symlet11
///<summary>
/// Already orthonormal coefficients taken from Filip Wasilewski's webpage
/// http://wavelets.pybytes.com/wavelet/sym12/ Thanks!
///</summary>
///<remarks>
/// Christian ([email protected]) 17.08.2014 14:06:57
///</remarks>
public class Symlet12 : Wavelet {
///<summary>
/// Constructor calculating analytically the orthogonal Symlet wavelet,
/// orthonormalizes them (normed, due to ||*||2 euclidean norm), sets
// the scaling coefficients, and the orthonormal bases afterwards.
///</summary>
///<remarks>
/// Christian ([email protected]) 16.02.2014 13:40:30
///</remarks>
public Symlet12( ) : base( "Symlet 12", 24, 2) {
_scalingDeCom[ 0 ] = 0.00011196719424656033;
_scalingDeCom[ 1 ] = -1.1353928041541452e-05;
_scalingDeCom[ 2 ] = -0.0013497557555715387;
_scalingDeCom[ 3 ] = 0.00018021409008538188;
_scalingDeCom[ 4 ] = 0.007414965517654251;
_scalingDeCom[ 5 ] = -0.0014089092443297553;
_scalingDeCom[ 6 ] = -0.024220722675013445;
_scalingDeCom[ 7 ] = 0.0075537806116804775;
_scalingDeCom[ 8 ] = 0.04917931829966084;
_scalingDeCom[ 9 ] = -0.03584883073695439;
_scalingDeCom[ 10 ] = -0.022162306170337816;
_scalingDeCom[ 11 ] = 0.39888597239022;
_scalingDeCom[ 12 ] = 0.7634790977836572;
_scalingDeCom[ 13 ] = 0.46274103121927235;
_scalingDeCom[ 14 ] = -0.07833262231634322;
_scalingDeCom[ 15 ] = -0.17037069723886492;
_scalingDeCom[ 16 ] = 0.01530174062247884;
_scalingDeCom[ 17 ] = 0.05780417944550566;
_scalingDeCom[ 18 ] = -0.0026043910313322326;
_scalingDeCom[ 19 ] = -0.014589836449234145;
_scalingDeCom[ 20 ] = 0.00030764779631059454;
_scalingDeCom[ 21 ] = 0.002350297614183465;
_scalingDeCom[ 22 ] = -1.8158078862617515e-05;
_scalingDeCom[ 23 ] = -0.0001790665869750869;
_buildBaseSystem( );
} // Symlet12
} // Symlet12
} // namespace