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We address the problem of estimating the instantaneous frequency (IF) of a phase signal using its level-crossing (LC) information based on front-end auditory processing motivation. We show that the problem of IF estimation using LC information can be cast in the framework of estimation from irregularly sampled data. The formulation has the generality of estimating different types of IF without the need for a quasistationary assumption. We consider two types of IF-polynomial and bandlimited; we use polynomial interpolating functions for the former, and for the latter, we propose a novel "line plus sum of sines" model. The model parameters are estimated by linear regression. Considering the noisy case, LC data for different levels is analyzed, and methods for combining different estimators from LCs are discussed. Theoretical and extensive simulation results show that the performance of the zero-crossing (ZC) based IF estimator and the level-crossing based IF estimator with smaller level values is better than those obtained with higher level values or their combinations. The new technique reaches the Crame´r-Rao bound (CRB) roughly above 4 dB signal-to-noise ratio (SNR), and its performance does not deteriorate rapidly with mismatch in the IF order compared with the other techniques in the literature.