makebsfilter.sci

小波分解源代码

function [qmf,dqmf] = MakeBSFilter(Type,Par)
// MakeBSFilter -- Generate Biorthonormal QMF Filter Pairs
//  Usage
//    [qmf,dqmf] = MakeBSFilter(Type,Par)
//  Inputs
//    Type   string, one of:
//             'Triangle'
//             'Interpolating' 'Deslauriers' (the two are same)
//             'Average-Interpolating'
//             'CDF' (spline biorthogonal filters in Daubechies's book)
//             'Villasenor' (Villasenor's 5 best biorthogonal filters)
//    Par    integer list, e.g. if Type ='Deslauriers', Par=3 specifies
//           Deslauriers-Dubuc filter, polynomial degree 3
//  Outputs
//    qmf    quadrature mirror filter  (odd length, symmetric)
//    dqmf   dual quadrature mirror filter  (odd length, symmetric)
//
//  See Also
//    FWT_PBS, IWT_PBS, FWT2_PBS, IWT2_PBS
//
//  References
//    I. Daubechies, "Ten Lectures on Wavelets."
//    
//    G. Deslauriers and S. Dubuc, "Symmetric Iterative Interpolating Processes."
//
//    D. Donoho, "Smooth Wavelet Decompositions with Blocky Coefficient Kernels."
// 
//    J. Villasenor, B. Belzer and J. Liao, "Wavelet Filter Evaluation for
//    Image Compression."
//
//  Copyright Aldo I Maalouf

	[lhs,rhs]=argn(0);
	if rhs < 2,
	  Par = 0;
	end
	
	sqr2 = sqrt(2);	
	
	if Type=='Triangle',
	  qmf = [0 1 0];
	  dqmf = [.5 1 .5];
	  
	elseif Type=='Interpolating' | Type=='Deslauriers',
	  qmf  = [0 1 0];
	  dqmf = MakeDDFilter(Par)';
	  dqmf =  waverow(dqmf(1:(length2(dqmf)-1)));
	  
	elseif Type=='Average-Interpolating',
	  qmf  = [0 .5 .5] ;
	  dqmf = [0 ; MakeAIFilter(Par)]';
	  
	elseif Type=='CDF',
	  if Par(1)==1,
	    dqmf = [0 .5 .5] .* sqr2;
	    if Par(2) == 1,
	      qmf = [0 .5 .5] .* sqr2;
	    elseif Par(2) == 3,
	      qmf = [0 -1 1 8 8 1 -1] .* sqr2 / 16;
	    elseif Par(2) == 5,
	      qmf = [0 3 -3 -22 22 128 128 22 -22 -3 3].*sqr2/256;
	    end
	  elseif Par(1)==2,
	    dqmf = [.25 .5 .25] .* sqr2;
	    if Par(2)==2,
	      qmf = [-.125 .25 .75 .25 -.125] .* sqr2;
	    elseif Par(2)==4,
	      qmf = [3 -6 -16 38 90 38 -16 -6 3] .* (sqr2/128);
	    elseif Par(2)==6,
	      qmf = [-5 10 34 -78 -123 324 700 324 -123 -78 34 10 -5 ] .* (sqr2/1024);
	    elseif Par(2)==8,
	      qmf = [35, -70, -300, 670, 1228, -3126, -3796, 10718, 22050, ...
		    10718, -3796, -3126, 1228, 670, -300, -70, 35 ] .* (sqr2/32768); 
	    end
	  elseif Par(1)==3,
	    dqmf = [0 .125 .375 .375 .125] .* sqr2;
	    if Par(2) == 1,
	      qmf = [0 -.25 .75 .75 -.25] .* sqr2;
	    elseif Par(2) == 3,
	      qmf = [0 3 -9 -7 45 45 -7 -9 3] .* sqr2/64;
	    elseif Par(2) == 5,
	      qmf = [0 -5 15 19 -97 -26 350 350 -26 -97 19 15 -5] .* sqr2/512;
	    elseif Par(2) == 7,
	      qmf = [0 35 -105 -195 865 363 -3489 -307 11025 11025 -307 -3489 363 865 -195 -105 35] .* sqr2/16384;
	    elseif Par(2) == 9,
	      qmf = [0, -63, 189, 469, -1911, -1308, 9188, 1140, -29676, 190, 87318, 87318, 190, -29676, ...
	      1140, 9188, -1308, -1911, 469, 189, -63] .* sqr2/131072;
	    end
	  elseif Par(1)==4,
	    dqmf = [.026748757411, -.016864118443, -.078223266529, .266864118443, .602949018236, ...
		  .266864118443, -.078223266529, -.016864118443, .026748757411] .*sqr2;
	    if Par(2) == 4,
	      qmf = [0 -.045635881557, -.028771763114, .295635881557, .557543526229, ...
		    .295635881557, -.028771763114, -.045635881557, 0] .*sqr2;
	    end
	  end
	  
	elseif Type=='Villasenor',
	  if Par == 1,
	    // The "7-9 filters"
	    qmf = [.037828455506995, -.023849465019380, -.11062440441842, .37740285561265];
	    qmf = [qmf .85269867900940 reverse(qmf)];
	    dqmf = [-.064538882628938 -.040689417609558 .41809227322221];
	    dqmf = [dqmf .78848561640566 reverse(dqmf)];
	  elseif Par == 2,
	    qmf  = [-.008473, .003759, .047282, -.033475, -.068867, .383269, .767245, .383269, -.068867,...
		  -.033475, .047282, .003759, -.008473];
	    dqmf = [0.014182  0.006292 -0.108737 -0.069163 0.448109 .832848 .448109 -.069163 -.108737 .006292 .014182];
	  elseif Par == 3,
	    qmf  = [0 -.129078 .047699 .788486 .788486 .047699 -.129078];
	    dqmf = [0 .018914 .006989 -.067237 .133389 .615051 .615051 .133389 -.067237 .006989 .018914];
	  elseif Par == 4,
	    qmf  = [-1 2 6 2 -1] / (4*sqr2);
	    dqmf = [1 2 1] / (2*sqr2);
	  elseif Par == 5,
	    qmf  = [0 1 1]/sqr2;
	    dqmf = [0 -1 1 8 8 1 -1]/(8*sqr2);
	  end
	end
	endfunction