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symaux

Symlet wavelet filter computation

Syntax

W = SYMAUX(N,SUMW)
W = SYMAUX(N)
W = SYMAUX(N,1)
W = SYMAUX(N,0)
W = SYMAUX(N,1)

Description

Symlets are the Äúleast asymmetricÄù 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, ...

    Note   Instability may occur when N is too large.

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  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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