An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density $${{{N_0}} \over 2}$$. The received signal is passed through a filter with impulse response h(t). Let $${E_s}$$ and $${E_n}$$ denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter $$\left( {SN{R_{\max }}} \right)$$, which of the following holds?

A super heterodyne receiver operates in the frequency range of 58 MHz – 68 MHz. The intermediate frequency f_1F and local oscillator frequency f_L0 are chosen such that f_1F $$\leq$$ f_L0.It is required that the image frequencies fall outside the 58 MHz – 68 MHz band. The minimum required f_1F (in MHz) is ___________.

The open-loop transfer function of a unity-feedback control system is $$$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is __________.

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.

X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …

P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficients