GATE EC 2014 Question Paper (15-Feb-2014) (Shift 2)

The power spectral density of a real stationary random process (𝑡) is given by

S_X≤ft( f ) = ≤ft\{ {*20c 1/W, ≤ft| f | ≤ W\\ 0, ≤ft| f | > W } .

The value of the expectation $E\left[\pi X\left(t\right)X\left(t-\frac{1}{4W}\right)\right]$ is ______

In the figure, M(f) is the Fourier transform of the message signal m(t) where A = 100 Hz and B = 40 Hz. Given v(t) = cos (2πf${}_c$ t) and w(t) = cos (2π(f${}_c$ + A)t), where f${}_c$ > A. The cutoff frequencies of both the filters are f${}_c$.



The bandwidth of the signal at the output of the modulator (in Hz) is _______

If the electric field of a plane wave is

$\vec{E}\left(z,t\right)=\hat{x}3\cos \left(\omega t-kz+30^{\circ }\right)-\hat{y}4\sin \left(\omega t-kz+45^{\circ }\right)\left(mV/m\right)$

The polarization state of the plane wave is

In the transmission line shown, the impedance Zin (in ohms) between node A and the ground is _________.

For a rectangular waveguide of internal dimensions a × b (a > b), the cut-off frequency for the TE₁₁ mode is the arithmetic mean of the cut-off frequencies for TE₁₀ mode and TE₂₀ mode. If a = √5 cm, the value of b (in cm) is _______.