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 $${\,\left| f \right|\, \le \,\,3\,kHz}$$.

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

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

Which of the following signals is/are periodic?