2. Consider the baseband binary PAM system shown below. Consider the case when both channel noise and intersymbol interference are present at the same time. You are expected to design a system where the mean square error of the entire system is minimized. Assume that w(t) is a white noise with power spectral density equal to No/2 and the entire environment is stationary. In such a scenario, show that impulse response of the receive filter must satisfy Q* (f) C($) Sq(f) + No/2 where Q(f) is the combined response of the transmit filter (g(t)) and the channel (h(t)), Sq(f) is the Fourier transform of the temporal autocorrelation function of the sequence {q(kTi)}. = Input binary data lan) x() Channel, *o(1) y(1) y,) Pulse- amplitude modulator Say 1 if y(t;) > Transmit filter g(1) Receive filter c(0) Decision device h(1) Sample at time t; = iTo Say O if y(t;) Transmit filter g(1) Receive filter c(0) Decision device h(1) Sample at time t; = iTo Say O if y(t;)