CWT(Morlet) | momoiot

Radar

STFT vs. Wavelet Transform

In contrast to the fixed time-frequency resolution of STFT/FFT,

Wavelet transform employs time-scaled windows to provide multi-resolution analysis.

This framework effectively captures both transient anomalies and long-term periodic oscillations in non-stationary signals.

1. Morlet Wavelet Overview

The Morlet wavelet transform employs a Morlet basis function which is complex sinusoidal signal windowed by a Gaussian envelope.

it can extracts amplitude and phase information, making it particularly effective for rhythmic and oscillatory signal analysis.

2. Signal Processing

By localized and scaled sinusoidal waveform, the transform varies its resolution across different frequencies, optimizing the capture of specific spectral components.

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 advanced time-frequency analysis.

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/frequency axis corresponds to different frequency ranges (inverse relationship), while the magnitude indicates the strength of each component.

4. Interpretation

(1) The transient rhythmic burst (10–20 Hz region) may represent a temporary oscillatory activity

such as human walking motion, rotating machinery vibration, or radar micro-Doppler generated by moving limbs.

(2)The continuously distributed low-frequency component may correspond to slow background motion or baseline oscillation,

such as platform vibration, body sway, engine rotation, or environmental low-frequency movement.

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.