A Sparse Time-Frequency Reconstruction Approach from the synchroextracting domain

Synchroextracting, including frequency-extracting and transient-extracting, offers a sparse time-frequency (TF) representation for multi-component signals. However, it is susceptible to amplitude modulation (AM) and frequency modulation (FM) when reconstructing the raw signal through the TF ridge. This paper proposes a new signal reconstruction approach (SRA) in the synchroextracting domain to address this limitation. This approach performs synchroextracting on the short-time Fourier transform (STFT) domain. We incorporate the extracting operator in the inverse STFT to establish the mathematical relationship between the synchroextracting representation and the retrieved signal, thus enabling the reconstruction of each mode in the synchroextracting domain. The proposed SRA is theoretically derived, and its reconstruction performance is evaluated in the frequency-extracting and transient-extracting domains. Two synthetic signals are utilized to demonstrate that compared with some advanced reconstruction methods, the SRA has a high reconstruction accuracy, strong noise robustness, and is less affected by AM-FM features and the window length. The application of the bat signal further clarifies the advantages of the SRA and its feasibility in practical applications. Moreover, this study also provides a new reconstruction framework and reference for other synchroextracting-type methods.