Polynomial Chirplet transform with application toinstantaneous frequency estimation

Abstract—In this paper, a new time–frequency analysis method known as the polynomial chirplet transform (PCT) is developed by extending the conventional chirplet transform (CT). By using a polynomial function instead of the linear chirp kernel in the CT, the PCT can produce a time–frequency distribution with excellent concentration for a wide range of signals with a continuous in-stantaneous frequency (IF). In addition, an effective IF estimation algorithm is proposed based on the PCT, and the effectiveness of this algorithm is validated by applying it to estimate the IF of a sig-nal with a nonlinear chirp component and seriously contaminated by a Gaussian noise and a vibration signal collected from a rotor test rig. Index Terms—Chirplet transform (CT), instantaneous fre-quency (IF), polynomial chirplet transform (PCT), short-time Fourier transform (STFT), time–frequency analysis. I