A method for analyze time-frequency of high-order synchronous extracted transform
signal includes such steps as expanding high-order Taylor series, carrying out short-time
Fourier transform, obtaininglocal instantaneous frequency, obtaining high-order instantaneous frequency, and obtaining high-order synchronous extracted operator, carrying out high-order Taylor
series expansion, carrying out short-time
Fourier transform, and obtaining high-order synchronous extracted operator. Finally, taking the frequency set after the short-time
Fourier transform as the
center frequency set, combined withthe high-order synchronous extraction operator, it 'extracts' the value of each time-frequency point corresponding to the instantaneous frequency in the vicinity of each
center frequency, that is, only the energy near the time-frequency
ridge in the time-frequency plane is reserved, and all the other divergent energy is eliminated to obtain the high-order synchronous extraction transform value. High-order synchronous extraction transform not only inherits the advantages of high time-frequency focusing and good
noise robustness of synchronous extraction transform, but also has higher time-frequency precision than short-time Fourier transform and synchronous extraction transform, so it is a new time-
frequency analysis method with high precision.