GATE EC 2016 Question Paper (31-Jan-2016) (Shift 2)

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal $x[n]=(2.0{)}^{|n|}$, $-\infty <n<+\infty$, then the ROC of its z-transform is represented by

Assume that the circuit in the figure has reached the steady state before time $t=0$ when the $3\Omega$ resistor suddenly burns out, resulting in an open circuit. The current $i(t)$ (in ampere) at $t=0^{+}$ is _____________

In the figure shown, the current $i$ (in ampere) is __________

The $z$ -parameter matrix $\left[\begin{array}{cc}{z}_{11}& z_{12}\\ z_{21}& z_{22}\end{array}\right]$ for the two-port network shown is

A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8$ kHz and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is to be computed in real time using the radix-$2$ decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes $20\mu s$ for computing each complex multiplication (including multiplications by $1$ and $-1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is ____________