# 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 ```