3.(Total=15%) Consider a communication system in which the received signal y(t)is given by
  

where w(t) is white Gaussian noise with (zero mean) power spectral densityN0/2 and s(t) is shown below

 At the receiver, the received signal y(t) is passed through a filter with impulseresponse h(t) = s(T-t). The output of the filter is sampled at time to that- provides a decision statistic Y with

 where

are thefiltered/sampled outputs of s(t) and w(t), respectively. The maximumlikelihood (ML) decision rule is then used based on Y to decide whether "I" or"0" is sent. Assume the noise process is independent of which signal is sent.
【題組】(a) (3%) Let t0 = 3 and T=4, i.e. h(t) = s(4- t). Determine the mean andvariance of the filtered and sampled noise term W.