Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and $$y\left( t \right)$$ band - limited to $$\,\left[ { - 1\,\,kHz,\,\,1kHz} \right].$$ For $$z\left( t \right)\,\, = \,x\left( t \right).y\left( t \right),$$ the Nyquist sampling frequency $$\left( {in\,\,kHz} \right)$$ is________.

A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output of the system $$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$

When y(0) = 1 and u(t) is a unit step function, y(t) is

A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \right.$$

Whjen a constant input of value 5 is applied to this filter, the steady state output is ____.