Wavelet Toolbox

Symlet Wavelets: symN

In symN, N is the order. Some authors use 2N 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 m₀ 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 z₁, 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 dbNs.

Daubechies Wavelets: dbN

Coiflet Wavelets: coifN

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