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Symlet wavelet filter computation
Syntax
Description
Symlets are the "least asymmetric" Daubechies wavelets.
W = SYMAUX(N,SUMW) is the order N Symlet scaling filter such that SUM(W) = SUMW. Possible values for N are 1, 2, 3, ...
W = SYMAUX(N) is equivalent to W = SYMAUX(N,1).
W = SYMAUX(N,0) is equivalent to W = SYMAUX(N,1).
Examples
% Generate wdb4 the order 4 Daubechies scaling filter.
wdb4 = dbaux(4)
wdb4 =
Columns 1 through 7
0.1629 0.5055 0.4461 -0.0198 -0.1323 0.0218 0.0233
Column 8
-0.0075
% wdb4 is a solution of the equation: P = conv(wrev(w),w)*2,
% where P is the "Lagrange à trous" filter for N=4.
% wdb4 is a minimum phase solution of the previous equation,
% based on the roots of P (see dbaux).
P = conv(wrev(wdb4),wdb4)*2;
% Generate wsym4 the order 4 symlet scaling filter.
% The Symlets are the "least asymmetric" Daubechies'
% wavelets obtained from another choice between the roots of P.
wsym4 = symaux(4)
wsym4 =
Columns 1 through 7
0.0228 -0.0089 -0.0702 0.2106 0.5683 0.3519 -0.0210
Column 8
-0.0536
% Compute conv(wrev(wsym4),wsym4) * 2 and check that wsym4
% is another solution of the equation P = conv(wrev(w),w)*2.
Psym = conv(wrev(wsym4),wsym4)*2;
err = norm(P-Psym)
err =
7.4988e-016
See Also
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| swt2 | symwavf | |
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