We will start with a simple wavelet: the `Mexican hat', shown on Fig. 2. We prefer to use the Mexican hat `upside-down', with a central trough (top of the hat) and two symmetric bumps on either side (the curled rim).
Figure 2: The Mexican hat wavelet
It is important to note that, for this to be a wavelet, the positive and negative areas `under' the curve must cancel out. This is known as the admissibility condition. Analytically, the Mexican hat wavelet is represented by
Selection of the wavelet shape is one of the important decisions on the user's part. It is similar to the choice of instruments of observation, like X-rays or filtered colored light or infra-red; or again like the selection of dyes as specific markers of biological tissues: each will show a part of the reality with specificity, and each reveals something that the others had concealed. This analogy has to be revised below: each view contains all the information!