Time-phase derivatives distribution for regular signal with the application in the parameters estimation of polynomial phase signal

A new concept-"Time-phase derivatives" distribution (TPDD) for the regular signal is presented and investigated in this paper. The TPDD is the extension form of the time-frequency distribution. The definitions of TPDD are given by the Exponential matched-phase transform (EMPT) and the High order bilinear matched-phase transform (HPT), and the corresponding TPDD illustrates the relationships of the phase derivatives, the time and the energy of the signal. Furthermore, the application of TPDD in the parameters estimation of Polynomial phase signal (PPS) is investigated. The results of Monte-Carlo simulations demonstrate that, the new approach can estimate the parameters with little computation and high precision.