| Wavelet Toolbox | |
Discussion
The deterministic part of the signal may undergo abrupt changes such as a jump, or a sharp change in the first or second derivative. In image processing, one of the major problems is edge detection, which also involves detecting abrupt changes. Also in this category, we find signals with very rapid evolutions such as transient signals in dynamic systems.
The main characteristic of these phenomena is that the change is localized in time or in space.
The purpose of the analysis is to determine:
The local aspects of wavelet analysis are well adapted for processing this type of event, as the processing scales are linked to the speed of the change.
Guidelines for Detecting Discontinuities
Short wavelets are often more effective than long ones in detecting a signal rupture. In the initial analysis scales, the support is small enough to allow fine analysis. The shapes of discontinuities that can be identified by the smallest wavelets are simpler than those that can be identified by the longest wavelets.
haar waveletThe presence of noise, which is after all a fairly common situation in signal processing, makes identification of discontinuities more complicated. If the first levels of the decomposition can be used to eliminate a large part of the noise, the rupture is sometimes visible at deeper levels in the decomposition.
Check, for example, the sample analysis File
Demo Analysisramp + white noise (MAT-file wnoislop). The rupture is visible in the level-six approximation (A6) of this signal.
| | Detecting Discontinuities and Breakdown Points I | Detecting Discontinuities and Breakdown Points II | |