dauborth.m Filter coefficients for Daubechies' compactly supported wavelets. Usage: [h0,h1,g0,g1] = dauborth(M) h0 - analysis scaling filter h1 - analysis wavelet filter, M/2 vanishing moments g0 - synthesis scaling filter g1 - synthesis wavelet filter Written by: Justin Romberg Created: 3/23/2004
0001 % dauborth.m 0002 % 0003 % Filter coefficients for Daubechies' compactly supported wavelets. 0004 % Usage: [h0,h1,g0,g1] = dauborth(M) 0005 % h0 - analysis scaling filter 0006 % h1 - analysis wavelet filter, M/2 vanishing moments 0007 % g0 - synthesis scaling filter 0008 % g1 - synthesis wavelet filter 0009 % 0010 % Written by: Justin Romberg 0011 % Created: 3/23/2004 0012 0013 function [h0,h1,g0,g1] = dauborth(M) 0014 0015 if (mod(M,2) ~= 0) 0016 error('M must be even.') 0017 end 0018 0019 [P,Q] = daubpoly(M/2); 0020 0021 qr = sort(roots(Q)); 0022 hr = [-ones(M/2,1); qr(1:M/2-1)]; 0023 gr = [-ones(M/2,1); qr(M/2:M-2)]; 0024 0025 h0p = poly(hr); 0026 g0p = poly(gr); 0027 h0 = sqrt(2)*h0p/sum(h0p); 0028 g0 = sqrt(2)*g0p/sum(g0p); 0029 h1 = (-1).^(1:M).*g0; 0030 g1 = (-1).^(0:M-1).*h0; 0031 0032 % flip h0 and g0 to produce functions in the text 0033 % h0 = fliplr(h0); 0034 % g0 = fliplr(g0); 0035 % h1 = (-1).^(1:M).*g0; 0036 % g1 = (-1).^(0:M-1).*h0; 0037 0038 % another source: http://wavelets.pybytes.com/wavelet/db4/