In a digital communication system, transmissions of successive bits through a noisy channel are assumed to be independent events with error probability p. The probability of at most one error in the transmission of an 8 - bit sequence is

The transfer function of a zero - order hold is

The message bit sequence input to a DPSK modulator is 1, 1, 0, 0, 1, 1. The carrier phase during the reception of the first two message bits is $$\pi ,\,\,\pi $$. The carrier phase for the remaining four message bits is

White Gaussian noise with zero mean and double - sided power spectral density $$\eta /2$$ is the input $$x(t)$$ to a linear system with impulse response $$h(t)$$ $$ = exp\left( { - t/RC} \right)\,\,\,\,\,\,\,\,u\left( t \right)$$. The output is $$y(t)$$ . Evaluate $$E\left[ {x\left( {t + \tau } \right)y\left( t \right)} \right]$$ for $$\tau > 0.$$ (Note: $$u(t)$$ is the unit step function)