symaux

Purpose

Symlet wavelet filter computation

Syntax

• W = SYMAUX(N,SUMW)
  

W = SYMAUX(N)

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

symwavf, wfilters

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