Local maximum multisynchrosqueezing transform and its application

The synchrosqueezing technique is widely used for analyzing the time variations of non-stationary signals. Recently, the local maximum synchrosqueezing transform (LMSST) method has been presented to effectively improve the time-frequency (TF) representation, which seems to be a promising tool. However, the LMSST is unable to accurately characterize the amplitude of strongly non-stationary signals, making it rather challenging to extract accurate TF information for signals with strong frequency modulation. Therefore, there is a significant barrier preventing the development of more precise and sharper results from the micro-Doppler signals with strong frequency modulation and multi-component characteristics. To overcome this problem, we coined a novel LMSST method, namely local maximum multisynchrosqueezing transform (LMMSST). The LMMSST is on the basis of local maximizing TF reassignment and multiple synchrosqueezing operators in which an iterated redistribution program is used to concentrate the ambiguous TF energy with a stepwise approach. As a result, the LMMSST significantly enhances the concentration in terms of energy of TF results and performs better in addressing strong frequency modulation and multi-component signals. In addition, it also allows perfect signal reconstruction and accurate estimating of the instantaneous frequency. Numerical results and application cases verify the effectiveness of the LMMSST method.