Wavelet Toolbox

Scale aspects

As a complement to the spectral signal analysis, new signal forms appear. They are less regular signals than the usual ones.

The cusp signal presents a very quick local variation. Its equation is t^r with t close to 0 and 0 < r < 1. The lower r the sharper the signal.

To illustrate this notion physically, imagine you take a piece of aluminum foil; The surface is very smooth, very regular. You first crush it into a ball, and then you spread it out so that it looks like a surface. The asperities are clearly visible. Each one represents a two-dimension cusp and analog of the one dimensional cusp. If you crush again the foil, more tightly, in a more compact ball, when you spread it out, the roughness increases and the regularity decreases.

Several domains use the wavelet techniques of regularity study:

• Biology for cell membrane recognition, to distinguish the normal from the pathological membranes
• Metallurgy for the characterization of rough surfaces
• Finance (which is more surprising), for detecting the properties of quick variation of values
• In Internet traffic description, for designing the services size

Wavelet Applications

Time aspects