List of top Signals and Systems Questions asked in GATE Electrical Engineering

Let an input \( x(t) = 2\sin(10\pi t) + 5\cos(15\pi t) + 7\sin(42\pi t) + 4\cos(45\pi t) \) be passed through an LTI system having an impulse response, \[ h(t) = 2\left(\frac{\sin(10\pi t)}{\pi t}\right) \cos(40\pi t). \] The output of the system is

An LTI system is shown in the figure where \[ G(s) = \frac{100}{s^2 + 0.1s + 10} \] The steady state output of the system, to the input \( r(t) \), is given as \[ y(t) = a + b \sin(10t + \theta) \] The values of 'a' and 'b' will be

If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is ________. (round off to nearest integer)