GATE EC 2016 Question Paper (30-Jan-2016) (Shift 1)

The open-loop transfer function of a unity-feedback control system is given by

$\mathrm{G}\left(\mathrm{s}\right)=\frac{\mathrm{K}}{\mathrm{s}\left(\mathrm{s}+2\right)}$

For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is ____________.

The transfer function of a linear time invariant system is given by

$\mathrm{H}(\mathrm{s})=2{\mathrm{s}}^4-5{\mathrm{s}}^3+5s+2$

The number of zeros in the right half of the s-plane is ________.

Consider a discrete memory less source with alphabet S = s₀, s₁, s₂, s₃, s₄, ... and respective probabilities of occurrence P = {1/2, 1/4, 1/8, 1/16, 1/32, .......}. The entropy of the source (in bits) is _______.

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1. Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is ________.

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 $\frac{{\mathrm{N}}_0}{2}$. The received signal is passed through a filter with impulse response h(t). Let 𝐸${}_{\text{s}}$ and 𝐸${}_{\text{h}}$ 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 (SNR${}_{max}$), which of the following holds?