2. Principle

The Mexican Hat Wavelet operates by correlating the signal with scaled and shifted versions of the Mexican Hat wavelet.

By adjusting the scale and position of the wavelet, it extracts localized signal features, emphasizing local variations rather than repetitive signal patterns.

 

– Illustration: scaling and shifting of the wavelet function

 

 

 

 

3. Representation

The result of the Mexican Hat Wavelet Transform is represented as a scalogram, which shows the magnitude of signal components across time and scale.

The scale axis corresponds to different frequency ranges, while the magnitude highlights localized signal features.

 

-.Illustration: scalogram (time vs scale vs magnitude)

 

 

 

 

4. Interpretation

In the scalogram, high-intensity regions indicate localized changes or sharp features in the signal.

The distribution across time and scale highlights transient events and structural variations.

 

– Illustration: time-scale pattern example

 

 

 

 

5. Radar Application

In radar systems, the Mexican Hat Wavelet is used to detect transient events and localized signal variations.

Compared to the Morlet Wavelet, it is more sensitive to abrupt changes but provides less detailed frequency information.

It is particularly useful when detecting abrupt changes rather than continuous frequency patterns.