Appendix A

The wavelet coefficients in a discontinuous function.

The local regularity changes can be therefore highlighted by means of the amplitude wavelet coefficients. Using the signal presented in (Daubechies, 1992, p.301), we constructed the following example to illustrate the propriety.

Considering,

This function is continuous except in x = -1, the first derivative of it is discontinuous at that point and in the point x = 0 and the second derivative is discontinuous at these points. We compute one decomposition level of discrete orthogonal wavelet transform using a Daubechies wavelet of order 2. The result is presented in the Figure A.6, the larger amplitude of the wavelet coefficients, identifies the three points where the signal has changes in the local regularity.