For the circuit shown below different time constants are given :

1. 1. $0.5 \times 10^{-3} \mathrm{sec}$

2. 2. $2 \times 10^{-3} \mathrm{sec}$

3. 3. $0.25 \times 10^{-3} \mathrm{sec}$

4. 4. $10^{-3} \mathrm{sec}$

What are the charging and discharging times respectively :

If G(f) represents the Fourier transform of a signal g (t) which is real and odd symmetric in time, then

A low pass signal x(t) has a spectrum given by $$X(f) = \left\{ {\matrix{ {1 - \left| f \right|/2000,} & {for\,\,\left| f \right|\, \le \,2000\,Hz} \cr {0,} & {elsewhere} \cr } } \right.$$
Assuming that x(t) is ideally sampled at a sampling frequency of 3 kHz, sketch
(i) x(f), and
(ii) the spectrum of the sampled signal for $${\,\left| f \right|\, \le \,\,3\,kHz}$$.

A linear discrete - time system has the characteristic equation, $${z^3} - 0.81\,\,z = 0.$$ The system