High-Performance Time-Frequency Distribution Reconstruction Based on Adaptive Short-Time Chirplet Decomposition

‍ ‍The spectrum obtained by Fourier transform （FT） could clearly reflect the frequency component contained in the signal， but was not able to reveal the time-varying characteristics of the instantaneous frequency function. In order to meet the analysis requirements of a large number of non-stationary signals in engineering applications， time-frequency （TF） analysis （TFA） methods， which could simultaneously describe the characteristics of signals in the time domain and the frequency domain， had been widely concerned and deeply studied. However， the TF distribution （TFD） obtained by traditional TFA methods were difficult to express the signal’s TF feature precisely due to the poor energy concentration and serious cross-term interference. The quality of the signal’s TFD could be effectively improved by utilizing the inherent sparsity of the signal. In this paper， the essence of the sparse TF decomposition was clarified through the Taylor expansion of the signal’s phase function， and the shortcomings of existing sparsity-based TFA algorithms were fully analyzed. On this basis， a reconstruction method of the high-performance TFD based on the adaptive short-time Chirplet decomposition （ASTCD） was proposed. Firstly， the optimal short-time signal segment with the strongest quasi-stationary property was generated for each time instant by using the window whose width had been set to be adaptively varying with the signal’s TF feature. Secondly， a simplified design scheme of the Chirplet dictionary was proposed and the obtained Chirplet dictionary was employed for the sparse decomposition of the above-mentioned short-time signal segments. Moreover， the results of the sparse decomposition were further employed to realize the parametric reconstruction of the instantaneous spectrum of the short-time signal’s center time instant. Finally， the high-performance cross-term-free TFD with high energy concentration was generated by arranging all instantaneous spectra in chronological order. Simulation results confirmed that the proposed method can effectively overcome the TF pattern distortion problem， which is experienced by existing sparsity-based TFA methods. At the same time， great advantages in computational efficiency can be also obtained by the proposed method. In addition， an actual radar system was used to collect the echo of the micro-motion target， which is further processed by the proposed method to verify its effectiveness and application potential.