Multicomponent decomposition of a time-varying acoustic Doppler signal generated by a passing railway vehicle using Complex Shifted Morlet Wavelets

• Wayside condition monitoring for planned maintenance.
• An invariance approach for multicomponent decomposition of time-varying signals.
• Estimation of the instantaneous frequency of time-varying acoustic Doppler signals.
• A cluster of CSM wavelets is applied to appropriate ranges in the frequency domain.
• The CSM wavelet allows the selection of the wavelet center frequency and bandwidth.

Complex Shifted Morlet Wavelets (CSMW) present a number of advantages, since the concept of shifting the Morlet wavelet in the frequency domain allow the simultaneous optimal selection of both the wavelet center frequency and the wavelet bandwidth. According to the proposed method, a cluster of CSMW wavelets is used, covering appropriate ranges in the frequency domain. Then, instead of directly processing the instantaneous frequency of each CSMW, an invariance approach is used to indirectly recover the individual harmonic components of the signal. This invariance approach is based actually on the same rotational approach, using the same matrix properties, which consists the core of the well known ESPRIT algorithm. Moreover, the DESFRI (DEtection of Source Frequencies via Rotational Invariance) approach is introduced to support the proposed CSMW method to semi-automated selection of the center frequency of the applied Morlet window. This approach is based on the singular values that are extracted as an intermediate product of the proposed decomposition process. By the application of the method in a multi-component synthetic signal a way to select the critical parameters of the Morlet wavelet, is investigated. The method is further tested on a time-varying acoustic Doppler signal generated by a passing railway vehicle, indicating promising results for the estimation of the variable instantaneous frequency and the multi-component decomposition of it.