Consider the optimum detection of the sinusoidal signal in AWGN:
![619_Equation 5.jpg](https://secure.tutorsglobe.com/CMSImages/619_Equation%205.jpg)
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 exactly the same only at the time instant t = T.