Wavelet Toolbox |

**Symlet Wavelets: symN**

In *symN*, *N* is the order. Some authors use 2*N* instead of *N*. Symlets are only near symmetric; consequently some authors do not call them symlets. More about symlets can be found in [Dau92], pages 194, 254-257. By typing `waveinfo('sym')`

at the MATLAB command prompt, you can obtain a survey of the main properties of this family.

**Figure 6-13: Symlets sym4 on the Left and sym8 on the Right
**

Daubechies proposes modifications of her wavelets that increase their symmetry can be increased while retaining great simplicity.

The idea consists of reusing the function *m*_{0} introduced in the *dbN*, considering the as a function *W* of .

Then we can factor *W* in several different ways in the form of

because the roots of *W* with modulus not equal to 1 go in pairs. If one of the roots is *z*_{1}, then is also a root.

- By selecting
*U*such that the modulus of all its roots is strictly less than 1, we build Daubechies wavelets*dbN*. The*U*filter is a "minimum phase filter." - By making another choice, we obtain more symmetrical filters; these are symlets.

The symlets have other properties similar to those of the *dbN*s.

Daubechies Wavelets: dbN | Coiflet Wavelets: coifN |

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