New approaches for chirplet approximation

This correspondence proposes efficient algorithms for approximating complex-valued and real-valued signals as a weighted sum of multiple chirplet atoms, which are characterized by four parameters, namely the scale, time, frequency, and chirp rate. Direct sequential estimation of the parameters of multiple chirplets causes error propagations, i.e., the estimated parameters of the initial chirplets significantly affect the parameter estimation of the subsequent chirplets and may result in large chirplet approximation errors. To deal with this problem, we further exploit a relaxation (RELAX) method for recursive chirplet parameter estimation. RELAX can be used in conjunction with time-domain or frequency-domain algorithms to improve the parameter estimation accuracy for multiple chirplets. Unlike previous methods, our chirplet approximations require neither any a priori complete dictionary of chirplets nor complicated multidimensional searches to obtain suitable choices of chirplet parameters. The effectiveness of the proposed approaches is demonstrated via a number of simulated examples.