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antenna approximation arrival assumed autocovariance function average likelihood ratio average risk bandwidth Bayes criterion bias level carrier frequency coefficients complex autocovariance complex envelope components computed covariances decision surface defined derived detection probabilities detection system determined eigenfunctions eigenvalues envelope V(t error false-alarm and detection false-alarm probability Q0 filter matched formula Fourier transform frequency modulation given by eq hypothesis H0 impulse response input v(t integral equation joint p.d.f. kernel large number least favourable distribution likelihood ratio matched filter maximum maximum-likelihood estimate mean value measured method minimax narrow-band signals Neyman-Pearson criterion observation interval optimum peak power spectrum prior p.d.f. prior probabilities probability density function probability of detection pulse quadratic detector quantity radar result Section signal amplitudes signal is present signal s(t signal-to-noise ratio solution statistically independent stochastic process strategy target theory transfer function variance vectors white noise Y(co zero