MPD.rar_MPD_basis pursuit_data analysis_seismic_spectral method

function f = MakeONFilter(Type,Par) % MakeONFilter -- Generate Orthonormal QMF Filter for Wavelet Transform % Usage % qmf = MakeONFilter(Type,Par) % Inputs % Type string, 'Haar', 'Beylkin', 'Coiflet', 'Daubechies', % 'Symmlet', 'Vaidyanathan','Battle' % Par integer, it is a parameter related to the support and vanishing % moments of the wavelets, explained below for each wavelet. % % Outputs % qmf quadrature mirror filter % % Description % The Haar filter (which could be considered a Daubechies-2) was the % first wavelet, though not called as such, and is discontinuous. % % The Beylkin filter places roots for the frequency response function % close to the Nyquist frequency on the real axis. % % The Coiflet filters are designed to give both the mother and father % wavelets 2*Par vanishing moments; here Par may be one of 1,2,3,4 or 5. % % The Daubechies filters are minimal phase filters that generate wavelets % which have a minimal support for a given number of vanishing moments. % They are indexed by their length, Par, which may be one of % 4,6,8,10,12,14,16,18 or 20. The number of vanishing moments is par/2. % % Symmlets are also wavelets within a minimum size support for a given % number of vanishing moments, but they are as symmetrical as possible, % as opposed to the Daubechies filters which are highly asymmetrical. % They are indexed by Par, which specifies the number of vanishing % moments and is equal to half the size of the support. It ranges % from 4 to 10. % % The Vaidyanathan filter gives an exact reconstruction, but does not % satisfy any moment condition. The filter has been optimized for % speech coding. % % The Battle-Lemarie filter generate spline orthogonal wavelet basis. % The parameter Par gives the degree of the spline. The number of % vanishing moments is Par+1. % % See Also % FWT_PO, IWT_PO, FWT2_PO, IWT2_PO, WPAnalysis % % References % The books by Daubechies and Wickerhauser. % if strcmp(Type,'Haar'), f = [1 1] ./ sqrt(2); end if strcmp(Type,'Beylkin'), f = [ .099305765374 .424215360813 .699825214057 ... .449718251149 -.110927598348 -.264497231446 ... .026900308804 .155538731877 -.017520746267 ... -.088543630623 .019679866044 .042916387274 ... -.017460408696 -.014365807969 .010040411845 ... .001484234782 -.002736031626 .000640485329 ]; end if strcmp(Type,'Coiflet'), if Par==1, f = [ .038580777748 -.126969125396 -.077161555496 ... .607491641386 .745687558934 .226584265197 ]; end if Par==2, f = [ .016387336463 -.041464936782 -.067372554722 ... .386110066823 .812723635450 .417005184424 ... -.076488599078 -.059434418646 .023680171947 ... .005611434819 -.001823208871 -.000720549445 ]; end if Par==3, f = [ -.003793512864 .007782596426 .023452696142 ... -.065771911281 -.061123390003 .405176902410 ... .793777222626 .428483476378 -.071799821619 ... -.082301927106 .034555027573 .015880544864 ... -.009007976137 -.002574517688 .001117518771 ... .000466216960 -.000070983303 -.000034599773 ]; end if Par==4, f = [ .000892313668 -.001629492013 -.007346166328 ... .016068943964 .026682300156 -.081266699680 ... -.056077313316 .415308407030 .782238930920 ... .434386056491 -.066627474263 -.096220442034 ... .039334427123 .025082261845 -.015211731527 ... -.005658286686 .003751436157 .001266561929 ... -.000589020757 -.000259974552 .000062339034 ... .000031229876 -.000003259680 -.000001784985 ]; end if Par==5, f = [ -.000212080863 .000358589677 .002178236305 ... -.004159358782 -.010131117538 .023408156762 ... .028168029062 -.091920010549 -.052043163216 ... .421566206729 .774289603740 .437991626228 ... -.062035963906 -.105574208706 .041289208741 ... .032683574283 -.019761779012 -.009164231153 ... .006764185419 .002433373209 -.001662863769 ... -.000638131296 .000302259520 .000140541149 ... -.000041340484 -.000021315014 .000003734597 ... .000002063806 -.000000167408 -.000000095158 ]; end end if strcmp(Type,'Daubechies'), if Par==4, f = [ .482962913145 .836516303738 ... .224143868042 -.129409522551 ]; end if Par==6, f = [ .332670552950 .806891509311 ... .459877502118 -.135011020010 ... -.085441273882 .035226291882 ]; end if Par==8, f = [ .230377813309 .714846570553 ... .630880767930 -.027983769417 ... -.187034811719 .030841381836 ... .032883011667 -.010597401785 ]; end if Par==10, f = [ .160102397974 .603829269797 .724308528438 ... .138428145901 -.242294887066 -.032244869585 ... .077571493840 -.006241490213 -.012580751999 ... .003335725285 ]; end if Par==12, f = [ .111540743350 .494623890398 .751133908021 ... .315250351709 -.226264693965 -.129766867567 ... .097501605587 .027522865530 -.031582039317 ... .000553842201 .004777257511 -.001077301085 ]; end if Par==14, f = [ .077852054085 .396539319482 .729132090846 ... .469782287405 -.143906003929 -.224036184994 ... .071309219267 .080612609151 -.038029936935 ... -.016574541631 .012550998556 .000429577973 ... -.001801640704 .000353713800 ]; end if Par==16, f = [ .054415842243 .312871590914 .675630736297 ... .585354683654 -.015829105256 -.284015542962 ... .000472484574 .128747426620 -.017369301002 ... -.044088253931 .013981027917 .008746094047 ... -.004870352993 -.000391740373 .000675449406 ... -.000117476784 ]; end if Par==18, f = [ .038077947364 .243834674613 .604823123690 ... .657288078051 .133197385825 -.293273783279 ... -.096840783223 .148540749338 .030725681479 ... -.067632829061 .000250947115 .022361662124 ... -.004723204758 -.004281503682 .001847646883 ... .000230385764 -.000251963189 .000039347320 ]; end if Par==20, f = [ .026670057901 .188176800078 .527201188932 ... .688459039454 .281172343661 -.249846424327 ... -.195946274377 .127369340336 .093057364604 ... -.071394147166 -.029457536822 .033212674059 ... .003606553567 -.010733175483 .001395351747 ... .001992405295 -.000685856695 -.000116466855 ... .000093588670 -.000013264203 ]; end end if strcmp(Type,'Symmlet'), if Par==4, f = [ -.107148901418 -.041910965125 .703739068656 ... 1.136658243408 .421234534204 -.140317624179 ... -.017824701442 .045570345896 ]; end if Par==5, f = [ .038654795955 .041746864422 -.055344186117 ... .281990696854 1.023052966894 .896581648380 ... .023478923136 -.247951362613 -.029842499869 ... .027632152958 ]; end if Par==6, f = [ .021784700327 .004936612372 -.166863215412 ... -.068323121587 .694457972958 1.113892783926 ... .477904371333 -.102724969862 -.029783751299 ... .063250562660 .002499922093 -.011031867509 ]; end if Par==7, f = [ .003792658534 -.001481225915 -.017870431651 ... .043155452582 .096014767936 -.070078291222 ... .024665659489 .758162601964 1.085782709814 ... .408183939725 -.198056706807 -.152463871896 ... .005671342686 .014521394762 ]; end if Par==8, f = [ .002672793393 -.000428394300 -.021145686528 ... .005386388754 .069490465911 -.038493521263 ... -.073462508761 .515398670374 1.099106630537 ... .680745347190 -.086653615406 -.202648655286 ... .010758611751 .044823623042 -.000766690896 ... -.004783458512 ]; end if Par==9, f = [ .001512487309 -.000669141509 -.014515578553 ... .012528896242 .087791251554 -.025786445930 ... -.270893783503 .049882830959 .873048407349 ... 1.015259790832 .337658923602 -.077172161097 ... .000825140929 .042744433602 -.016303351226 ... -.018769396836 .000876502539 .001981193736 ]; end if Par==10,