Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by h(0)= $${1 \over 3};h\left[ 1 \right] = {1 \over 3};h\left[ 2 \right] = {1 \over 3};\,and\,h\,\left[ n \right]$$ =0 for n < 0 and n > 2. Let H ($$\omega $$) be the Discrete- time Fourier transform (DTFT) of h[n], where $$\omega $$ is the normalized angular frequency in radians. Given that ($${\omega _o}$$) = 0 and 0 < $${\omega _0}$$ < $$\pi $$, the value of $${\omega _o}$$ (in ratians ) is equal to ____________.

Consider the following statements for continuous-time linear time invariant (LTI) system.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$h(t) = \left\{ {{{2\sin (300\pi t)} \over {\matrix{ {\pi t} \cr {600} \cr } }}} \right.\,,\,\matrix{ t \cr t \cr } \,\matrix{ \ne \cr = \cr } \,\matrix{ 0 \cr 0 \cr } $$

Let y(t) be the output of this filter. The maximum value of $$\left| {y(t)} \right|$$ is ________________________.

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as
$$y\left[ n \right]\, = \left\{ {\matrix{ {n\left| {x\left[ n \right]} \right|,} & {for\,\,0 \le n \le 10} \cr {x\left[ n \right] - x\left[ {n - 1} \right],} & {otherwise,} \cr } } \right.$$

Which one of the following statements is true about the system?