Consider the optimum detection of the sinusoidal signal s (t) sin (8t/T), 0 t T,

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Consider the optimum detection of the sinusoidal signal s (t) sin (8πt/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.

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