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Underwater Acoustic Echo Time-Frequency Feature Extraction and Reconstruction using Second-order Synchrosqueezing Transform

Time-frequency analysis-based signal feature extraction has been well studied in the active sonar area in recent years. When the non-stationary signal is analyzed, traditional approach, such as short-time Fourier transform, cannot provide an excellent time or frequency resolution simultaneously on account of the uncertainty principle. Furthermore, acoustic echo is strongly influenced by multi-path channel and complex environment of shallow water. In this paper, an enhanced time-frequency analysis method named second-order synchrosqueezing transform is investigated here to extract underwater acoustic echo characteristics and reconstruct them. Second-order synchrosqueezing transform is able to extract and clearly depict components with time-varying spectrum, and furthermore it allows individual reconstruction of these components. Synchrosqueezing is performed in three steps. First, the continuous wavelet transform of the received signal is calculated. Second, an initial estimate of the demodulated frequency is calculated based on the first step. Finally, continuous wavelet transform is squeezed via reassignment. In this way, synchrosqueezing representation is obtained, which process is invertible. Furthermore, second-order operation aims to adapt synchrosqueezing transform to the superposition of perturbed linear chirps.