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function [PR,PO]=coef_prep(pflt)
%[PR,PO]=coef_prep(pflt)
%
% This function returns coefficients of given pre- and postfilters to be
% used in critical sampled preprocessing. For details see [SW].//返回的是预滤波与后滤波算子
%
% [SW] V. Strela and A. T. Walden, "Signal and Image Denoising via Wavelet
% Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet
% Transforms", Imperial College, Statistics Section,
% Technical Report TR-98-01 (1998).
%
% Input:
% pflt string of characters, name of the prefilter; for admissible
% names and brief descriptions of filters see below
%
% Output:
% PR 预滤波
% r by r*l real array, prefilter;
% r is the number of scaling functions,
% l is the number of coefficients in the prefilter;
% PR is organized as follows: PR=[P1 P2 ... Pl]
%
% PO 后滤波
% r by r*m real array, postfilter;
% m is the number of coefficients in the postfilter;
% PO is organized as follows: PO=[R1 R2 ... Rl]
%
% Admissible Names of the Prefilters and their Properties:
% (all names of the filter banks are from coef.m;
% r is the number of scaling functions,
% l is the number of coefficients in the prefilter,
% m is the number of coefficients in the postfilter,
% A is maximal approximation order preserved by the prefilter, see [SW])
%
% 'ghmap' biorthogonal interpolation prefilter for the 'ghm' multifilter
% bank (see [XGHS, SHSTH]); r=2, l=2, m=2, A=2 //双正交插值预滤波
%
% [XGHS] X.-G. Xia, J. S. Geronimo, D. P. Hardin, and B. W. Suter,
% "Design of prefilters for discrete multiwavelet transforms",
% IEEE Trans. on SP, 44 (1996) 25-35.
% [SHSTH] V. Strela, P. Heller, G. Strang, P. Topiwala, and C. Heil,
% "The application of multiwavelet filter banks to signal and
% image processing", IEEE Trans. on Image Proc. (1998).
%
% 'ghmorap' orthogonal approximating prefilter for the 'ghm' multifilter
% bank (see [HR]); r=2, l=2, m=2, A=2 //正交逼近预滤波
%
% [HR] D. P. Hardin and D. W. Roach, "Multiwavelet prefilters I:
% Orthogonal prefilters preserving approximation order p <= 2",
% preprint (1997).
%
% 'clap' biorthogonal interpolation prefilter for 'cl' multifilter
% bank (see [SW]); r=2, l=1, m=1, A=2
% 'bih5ap' biorthogonal interpolation prefilter for 'bih52s' or 'bih54n'
% multifilter bank (see [SW]); r=2, l=1, m=1, A=2
% 'bih3ap' biorthogonal interpolation prefilter for 'bih32s' multifilter
% bank (see [SW]); r=2, l=1, m=1, A=2
% 'sa4ap' orthogonal prefilter for 'sa4' multifilter bank (see [STT]);
% r=2, l=1, m=1, A=1
% [STT] L.-X. Shen, H. H. Tan, and J. Y. Tham, "Symmetric-antisymmetric
% orthonormal multiwavelets and related scalar wavelets",
% preprint (1997).
%
% 'bighm2ap' biorthogonal interpolation prefilter for 'bighm2' multifilter
% bank r=2, l=1, m=1, A=2
% 'id' orthogonal identity prefilter (is used with balanced
% multiwavelets, see [Se]) r=2, l=1, m=1 // 正交算子预滤波，用于平衡小波
%
% [Se] I. Selesnick, "Cardinal Multiwavelets and the Sampling Theorem",
% prerprint (1998).
%
% Example of Usage:
% [PR,PO]=coef_prep('sa4ap')
% Author: Vasily Strela
% COPYRIGHT 1997,98 by Vasily Strela
if strcmp(pflt,'ghmap') %%ghn多小波用双正交插值预滤波
PR=[3/(8*sqrt(2)) 10/(8*sqrt(2)) 3/(8*sqrt(2)) 0;
0 0 1 0];
PO=[0 1 0 0;
0 -3/10 4*sqrt(2)/5 -3/10];
elseif strcmp(pflt,'ghmorap') %%ghm多小波用正交逼近预滤波
PR=[0.11942337067748,0.99158171438258,0.04967860804828,-0.00598315472909;
-0.00598315472909,-0.04967860804828,0.9915817143825,-0.11942337067748];
PO(:,1:2)=PR(:,3:4)';
PO(:,3:4)=PR(:,1:2)';
elseif strcmp(pflt,'clap') %%cl多小波用双正交插值预滤波
PR=[1/4 1/4;
1/(1+sqrt(7)) -1/(1+sqrt(7))];
PO=[2 (1+sqrt(7))/2
2 -(1+sqrt(7))/2];
elseif strcmp(pflt,'bih5ap') %%双正交h5多小波用双正交插值预滤波
PR=[1/4 1/4;
-1 1];
PO=[2 -1/2
2 1/2];
elseif strcmp(pflt,'bih3ap') %%双正交h3多小波用双正交插值预滤波
PR=[1/4 1/4;
-1/15 1/15];
PO=[2 -15/2
2 15/2];
elseif strcmp(pflt,'sa4ap') %%sa4多小波用正交预滤波
PR=[1,1;
-1,1]/sqrt(2);
PO=[1,-1;
1,1]/sqrt(2);
elseif strcmp(pflt,'bighm2ap') %%双正交ghm多小波用双正交插值预滤波
PR=[1/4 1/4;
1/3 -1/3];
PO=[2 3/2
2 -3/2];
elseif strcmp(pflt,'id') %%平衡多小波，用于平衡多小波
PR=[1 0;
0 1];
PO=[1 0;
0 1];
elseif strcmp(pflt,'minial') %% for GHM multiwavelets
PR=[2*sqrt(2) -sqrt(2); 1 0 ];
PO=[0 1 ; -1/sqrt(2) 2 ];
elseif strcmp(pflt,'orap') %% for GHM multiwavelets the result seems bad
PR=(sqrt(6)/6)*[1-sqrt(2) 1+sqrt(2) ; 1+sqrt(2) -1+sqrt(2)];
PO=inv(PR);
end