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Unformatted text preview: MATCHED FILTER DETECTION AND MONTE CARLO SIMULATIONS EEE 554 FALL 2010 Consider the problem of detecting the presence of a sinusoid s ( t ) = cos(2 f t ), with known frequency f = 300 Hz, in noise. The noise is zero-mean additive white Gaussian noise (AWGN) (with independent and identically distributed samples) with known covariance C n = 2 I , where 2 = 1 and I is the identity matrix. The received signal r ( t ) has duration T d = 10 s. We use a two-hypothesis formulation, where the signal is present under under hypothesis H 1 and not present under hypothesis H : H : r ( t ) = n ( t ) H 1 : r ( t ) = s ( t ) + n ( t ) It can be shown that the optimal detector for a known signal in AWGN is the matched filter (MF) detector, that decides that the signal is present if = integraldisplay T d r ( t ) s * ( t ) dt = integraldisplay T d r ( t ) cos(2 300 t ) dt > , where is the detection threshold (that can be computed based on the desirable probability of false alarm). For this problem, assume thatalarm)....
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