Assume that the circuit in the figure has reached the steady state before time t = 0 when the 3 Ω 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 ______.

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 µs 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 __________.

A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-transform x(z). If Y (z)=X (-z) is the z-transform of another signal y$$\left[ n \right]$$, then