A binary baseband digital communication system employs the signal $$$p\left( t \right) = \left\{ {\matrix{ {{1 \over {\sqrt {{T_s}} }},} & {0 \le t \le {T_s}} \cr {0,} & {otherwise} \cr } ,} \right.$$$

for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $${\eta \over 2} = 2.5\, \times \,{10^{ - 5}}$$ Watt per Hz. If information at the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit energy $${E_b}$$ (in mJ/bit) necessary 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