Detection and estimation of generalized chirps using time-frequency representations

We propose techniques for the detection and parameter estimation of generalized chirps in the presence of noise. Generalized chirps are nonstationary signals characterized by group delays with specific dispersion law characteristics. Special cases of generalized chirps include linear chirps, and hyperbolic chirps that are Doppler-invariant signals. We optimally detect generalized chirps using generalized timeshift covariant quadratic time-frequency representations (QTFRs) such as hyperbolic QTFRs used for detecting hyperbolic chirps. We also propose the parameter estimation of generalized chirps, and specialize our simulation results to hyperbolic chirps. We combine phase unwrapping with linear regression of the phase data at high signal-to-noise ratios (SNRs) to produce very simple and unbiased estimators that attain the Cramer-Rao lower bounds on variance. Maximum likelihood estimation performs well at low SNRs, but at the cost, of high computational complexity