Multicomponent Signal Analysis Based on Polynomial Chirplet Transform

Chirplet transform (CT) is effective in characterization of instantaneous frequency (IF) for monocomponent linear-frequency-modulated signal. However, the CT is not suitable to analyze multicomponent signal with nonlinear-frequency-modulated component. In this paper, a time-frequency fusion technique based on polynomial CT (PCT) (TFPCT) is proposed to characterize the time-frequency structure of such signals. The TFPCT relies on the fact that the PCT is able to concentrate the energy closely along the IF of the monocomponent signal in time-frequency distribution (TFD). For multicomponent signal, the TFPCT first estimates the proper coefficients with respect to individual component and, second, produces a series of the TFD using the PCT. Each TFD has better energy concentration along the IF of one component. Then, in order to reduce the interference of unwanted component and preserve the component of interest, each TFD is filtered and grouped as an image. At last, the TFPCT combines these TFDs to be an eventual fused TFD, which has the energy concentrating closely along the IF of all components. Comparison with several conventional TFD methods on both numerical multicomponent signal and bat echolocation signal validates the potential and the effectiveness of the proposed method.