GATE EC 2014 Question Paper (16-Feb-2014) (Shift 2)

An M-level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 KHz. The bit rate is 200 kbps and the system characteristic is a raised-cosine spectrum with 100% excess bandwidth. The minimum value of M is

Consider a discrete-time channel 𝑌 = 𝑋 + 𝑍, where the additive noise 𝑍 is signal-dependent.

In particular, given the transmitted symbol 𝑋 ∈ {−𝑎, +𝑎} at any instant, the noise sample 𝑍 is chosen independently from a Gaussian distribution with mean 𝛽𝑋 and unit variance. Assume a threshold detector with zero threshold at the receiver.

When β = 0, the BER was found to be Q(a) = 1 × 10⁻⁸

$(Q\left(v\right)=\frac{1}{\sqrt{2\pi }}\underset{v}{\overset{\infty }{\int }}{e}^{-u^2/2}du$, and for v > 1, use $Q\left(v\right)\approx e^{-v^2/2})$

When β = -0.3, the BER is closest to

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let 𝜓${}_{\text{A}}$ and 𝜓${}_{\text{B}}$ be the electrostatic potentials at A and B, respectively. The value of 𝜓${}_{\text{B}}$ – 𝜓${}_{\text{A}}$ in Volts is ________.

Given $\vec{F}=z{\hat{a}}_x+x{\hat{a}}_y+y{\hat{a}}_z$. If S represents the portion of the sphere x² + y² + z² = 1 for z ≥ 0 then ${\int }_s\nabla \times \vec{F}\cdot \overrightarrow{ds}$ is ________

If $\vec{E}=-\left(2y^3-3y{z}^2\right)\hat{x}-\left(6x{y}^2-3x{z}^2\right)\hat{y}+\left(6xyz\right)\hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is