GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

Let (X₁, X₂) be independent random varibales. X₁ has mean 0 and variance 1, while X₂ has mean 1 and variance 4. The mutual information I(X₁; X₂) between X₁ and X₂ in bits is_______.

Which one of the following statements about differential pulse code modulation (DPCM) is true?

In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is the inter symbol interference zero?

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characterstic impedance is V(l) = e${}^{\text{–}yl+j\omega t}$ Volts, where l is the distance along the length of the cable in metres, γ = (0.1 + j40)m${}^{\text{–}1}$ is the complex propagation constant, and ω = 2π × 10⁹ rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/metre is ________.

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link