We propose a time-frequency formulation for the optimum detection of Gaussian signals in white Gaussian noise based on hyperbolic class quadratic time frequency representations (QTFRs) such as the Altes distribution. We apply the detection scheme successfully to hyperbolic chirps and slowly fluctuating hyperbolic point targets, and show that the estimation of the latter's unknown parameters depends upon the hyperbolic ambiguity function. We also propose a general class of receivers in the hyperbolic class that provides a coherent framework between existing classical and new detectors. Furthermore, we propose the estimation of the parameters of hyperbolic chirps using phase unwrapping with linear regression of the phase data that produces simple and unbiased estimators whose variance attains the Cramer-Rao lower bound at signal-to-noise ratios (SNRs) higher than 12 dB. In comparison, we show that the maximum likelihood estimation technique gives accurate estimates at lower SNR (<-1 dB), but at the cost of high computational complexity.
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