A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrelation function of $$X(t)$$ is $${R_x}\left( \tau \right),$$ then the autocorrelation function $${R_x}\left( \tau \right),$$ of the output $$Y(t)$$ is equal to

An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $${p_1}$$ = $${p_4}$$ = 0.125 and $${p_2}$$ =$${p_3}$$. The information rate (bits/sec) of the message source is ____________________

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is _________.

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;1\right)}$$ .The steady state error e_ss due to a unit step input is