2. Principle

The Morlet Wavelet operates by correlating the signal with scaled and shifted versions of the Morlet basis function.

By adjusting the scale and position of the wavelet, it extracts signal components at different resolutions, enabling time-frequency analysis.

– Illustration: scaling and shifting of the wavelet function

3. Representation

The result of the Morlet 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 (inverse relationship), while the magnitude indicates the strength of each component.

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

4. Interpretation

In the scalogram, high-intensity regions indicate dominant signal components at specific times and scales.

The distribution across time and scale reveals transient events and multi-resolution characteristics of the signal.

– Illustration: time-scale pattern example

5. Radar Application

In radar systems, the Morlet Wavelet is used to analyze non-stationary signals and time-varying patterns.

It is particularly useful for detecting transient behaviors and complex target signatures that are not easily captured by fixed-resolution methods.

Compared to STFT, the Morlet Wavelet provides multi-resolution analysis, offering better time resolution at high frequencies and better frequency resolution at low frequencies.