GATE EC 2015 Question Paper (01-Feb-2015) (Shift 1)

In the circuit shown, assume that the diodes D₁ and D₂ are ideal. The average value of voltage V${}_{ab}$ (in Volts), across terminals ‘a’ and ‘b’ is _______.

Suppose x[n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ±2j. Which one of the following statements is TRUE for the signal x[n]?

A realization of a stable discrete-time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is

Let $\tilde{x}\left[n\right]=1+\cos \left(\frac{\pi n}{8}\right)$ be a periodic signal with period 16. Its DFS coefficients are defined by a_k = 1/16_n = 0^15 x≤ft[ n ]^ ≤ft( - jπ /8kn ) for all k. The value of the coefficient a₃₁ is ________.

Consider a continuous-time signal defined as:

$x\left(t\right)=\left(\frac{\sin \left(\frac{\pi t}{2}\right)}{\left(\frac{\pi t}{2}\right)}\right)\ast \sum _{n=-\infty }^{\infty }\delta \left(t-10n\right)$

where ‘∗’ denotes the convolution operation and t is in seconds. The Nyquist sampling rate (in samples/sec) for x(t) is ______.