The minimum sampling frequency (in samples /sec) required to reconstruct the following signal from its samples without distortion $$x(t) = 5{\left( {{{\sin \,\,2\,\pi \,1000\,t)} \over {\pi \,t}}} \right)^3} + 7{\left( {{{\sin \,\,2\,\pi \,1000\,t} \over {\pi \,t}}} \right)^2}$$

would be

A low-pass filter having a frequency response $$H(j\omega )$$ = $$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if

In the system shown below,
x(t) = (sint)u(t). In steady-state, the response y(t) will be

A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The system is