Application Of Polynomial Chirplet Transform In Instantaneous Frequency Estimation

Instantaneous frequency is the basic parameter of time frequency mode, as an important role in frequency modulation signal, and it has been in the radar, detection, voice and other fields and won a wide range of applications. Research of instantaneous frequency estimation method and the corresponding parameter estimation has important practical value in time-frequency analysis, and the time-frequency distribution is the measurement tool of non-stationary signals, which can fully show the signal frequency variation law with time, and can be observed the degree of the signal energy and concentration in the time-frequency distribution.This paper first interprets the research background and the concept origin of the instantaneous frequency, and finally gives the common definition of instantaneous frequency. Secondly, this paper introduces the common time frequency analysis (TFA) methods:firstly, it introduces the short-time Fourier transform and Wigner-Ville distribution, however, both of the methods have their own defects, and cannot achieve the desired result that the signal has high energy as well as aggregation and the estimated instantaneous frequency is closer to the theoretical value. Then parameterized TFA methods that different from the above methods are described. The algorithm of the conventional chirplet transforms (CT) and the polynomial chirplet transform (PCT) is described in detail, and the selection of parameters is very important for the methods. Chirplet transform method introduces the concept of frequency rotation operator and shift operator, and uses additional chirplet parameters of kernel function to deal with linear chirp signal. And by extending its frequency shift operator and rotation operator, and replacing the chirp function, the basic theory of PCT is finally introduced and PCT can estimate the IF of a signal with a nonlinear chirp component.The main research object of this article is the application of parameterized TFA method-the polynomial chirplet transform in instantaneous frequency (IF) estimation. The core of this method is using a polynomial function to replace the linear chirp kernel in the CT, so the PCT is very suitable to analysis the non-stationary and nonlinear signal. To ensure the quality of time-frequency analysis, this paper proposed a signal-dependent iterative procedure to select parameters for the polynomial chirplet transform, adaptively. Termination condition of the algorithm is the Renyi information, and the Renyi information of time frequency representation (TFR) is calculated in each iteration. The iteration will be terminated when the Renyi information of the current iteration is bigger than that of the previous one, or the Renyi information keeps decrease until not evident. In addition, the algorithm takes advantage of the polynomial fitting method to better match the theoretical value, therefore it can better estimate the instantaneous frequency and parameters. In the end, several simulation tests are carried on several different target signals. Through observations, data analysis, adding noise and comparison, the validity and advantage of the algorithm in this paper is proved. The result is more ideal comparing with other estimation methods,...