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 ________________________.

A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\;n\omega_0t\right)$$$ If $$x\left(t\right)=-x\left(-t\right)=-x\left(t-\mathrm\pi/{\mathrm\omega}_0\right)$$, we can conclude that

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6$$\mathrm\pi$$ rad/s

For the three statements above, which one of the following is correct?

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 ____________.