Wavelet Toolbox

Example 6: A Step Signal

Analyzing wavelet: db2

Decomposition levels: 5

In this case, we are faced with the simplest example of a rupture (i.e., a step). The time instant when the jump occurs is equal to 500. The break is detected at all levels, but it is obviously detected with greater precision in the higher resolutions (levels 1 and 2) than in the lower ones (levels 4 and 5). It is very precisely localized at level 1, where only a very small zone around the jump time can be seen.

It should be noted that the reconstructed details are primarily composed of the basic wavelet represented in the initial time.

Furthermore, the rupture is more precisely localized when the wavelet corresponds to a short filter.

Figure 4-5: A Step Signal

	Example 6: A Step Signal
Addressed topics	Detecting breakdown points. Suppressing signals. Detecting long-term evolution. Identify the range width of the variations of details and approximations.
Further exploration	Use the coefficients of the FIR filter associated with the wavelet to check the values of D1. Replace the step by an impulse. Add noise to the signal and repeat the analysis.

Example 5: Polynomial + White Noise

Example 7: Two Proximal Discontinuities