In the $$RLC$$ circuit shown in the figure, the input voltage is given by v_i(t) = 2 cos(200t)+4 sin(500t). The output voltage v₀(t) is

The z-parameter matrix for the two-port network shown is $$$\left[ {\matrix{ {2\,j\,\omega } & {j\,\omega } \cr {j\,\omega } & {3\, + \,2\,j\,\omega } \cr } } \right]$$$ Where the entries are in $$\Omega $$. Suppose $$\,{Z_b}\,\left( {j\,\omega } \right) = {R_b} + j\,\omega $$ Then the value of $${R_b}$$ (in $$\Omega $$) equals _______________________3

If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation, then x(t) is equal to

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 __________.