Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications

We introduce a novel ridge detection algorithm for time-frequency (TF) analysis, particularly tailored for intricate nonstationary time series encompassing multiple non-sinusoidal oscillatory components. The algorithm is rooted in the distinctive geometric patterns that emerge in the TF domain due to such non-sinusoidal oscillations. We term this method $\mathit{\text{shape-adaptive}}\mathit{\text{mode}}\mathit{\text{decomposition-based}}\mathit{\text{multiple}}\mathit{\text{harmonic}}\mathit{\text{ridge}}\mathit{\text{detection}}$ ($\mathsf{\text{SAMD-MHRD}}$). A swift implementation is available when supplementary information is at hand. We demonstrate the practical utility of $\mathsf{\text{SAMD-MHRD}}$ through its application to a real-world challenge. We employ it to devise a cutting-edge walking activity detection algorithm, leveraging accelerometer signals from an inertial measurement unit across diverse body locations of a moving subject.