Local Maximum-Based Synchroextracting Transform With Adaptive Time-Varying Parameter in the Time-Frequency Chirp Rate Space

Postprocessing methods related to reassignment have caught much attention because of their effectiveness in improving the readability of early time-frequency (TF) representations. Most postprocessing methods assume that signal components are well-separated in the frequency direction; hence, it is difficult for them to characterize input signals with overlapping instantaneous frequency (IF), Based on the principle that overlapping IFs can be well-separated in the TF chirp rate (TFCR) space, in this study, the local maximum-based synchroextracting transform with time varying parameter is proposed to perform reassignment in the TFCR space for input signals with overlapping IFs. The proposed method can adaptively estimate time varying parameter according to the gradient of the maximum and energy concentration of the boundary in the frequency chirp rate plane, which makes local maximum-based reassignment robust in the TFCR space. Thereby, highly energy-concentrated TF results can be obtained via chip rate summation for signals with overlapping IFs. On the other hand, the ridge detection algorithm is extended to the TFCR space to avoid permutation error and then extract IFs exactly. In the meantime, signal reconstruction of the proposed method is proven. The numerical experiment shows that the proposed method is superior to the compared methods.