A sender transmits binary characters to a receiver in a digital communication system. The signal, s(t), see, is used by the sender to represent a binary one and the absence of this signal is used to...

A sender transmits binary characters to a receiver in a digital communication system. The signal, s(t), see, is used by the sender to represent a binary one and the absence of this signal is used to represent zero. We model the received signal, X(t), by

Where
  is Gaussian noise with spectral density R₀. Determine the impulse response of a matched causal filter and compute the SNR (signal-to-noise ratio) of the output signal.