A Geometry Study on Reassignment Method and Synchrosqueezing Transform

The reassignment method (RM) and synchrosqueezing transform (SST) belong to the post-processing time frequency analysis (TFA) methods that are designed to improve the ability of some classical TFA methods to locate the time-varying signals. The related theory analysis and engineering applications are well-established in many studies. This study is intended to provide the geometry explanations to the post-processing manners of RM and SST that makes the relative mathematic theory easier to be understood. Based on the different post-processing behaviors., it can be known that., the RM can generate the energy-concentrated TFA results but cannot reconstruct signal, and the SST sacrifices the TFA resolution to re-obtain the ability of reconstructing mono-component modes. Finally, a novel TFA method combining the advantages of RM and SST is proposed.