(Solution) - Consider the optimum detection of the sinusoidal signal s t -(2025 Original AI-Free Solution)

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Consider the optimum detection of the sinusoidal signal s (t) sin (8?t/T), 0 ? t ? T, in additive white Gaussian noise.
(a) Determine the correlator output assuming a noiseless input.
(b) Determine the corresponding matched filter output, assuming that the filter includes a delay T to make it causal.
(c) Hence show that these two outputs are the same only at time instant t = T.