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Electronics and Communication Microwave Communication Difficulty: Medium

If $$L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}},$$ then f(0 + ) and f(∞) are given by Consider the signal x(t) shown in the figure. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interval 0 to 4 sec. The slope of h(t) in the interval 3 < t < 4 sec is A periodic signal x(t) has a trigonometric Fourier series expansion $$x\left( t \right) = {a_0} + \sum\limits_{n = 1}^\infty {\left( {{a_n}\cos n{\omega _0}t + {b_n}\sin n{\omega _0}t} \right)} $$ If $$x\left( t \right) = - x\left( { - t} \right) = - x\left( {t - \frac{\pi }{{{\omega _0}}}} \right),$$ we can conclude that The input impedance of a short circuited line of length less than quarter wave length is purely If x 1 (t) = 2sinπt + cos4πt and x 2 (t) = 2sin5πt + 3sin13πt, then