List of top Signals and Systems Questions on Linear time invariant and causal systems asked in GATE EE

Consider the system as shown below \[ y(t) = x(e^t) \] The system is

Let a causal LTI system be governed by the following differential equation \[ y(t) + \frac{1}{4} \frac{dy}{dt} = 2x(t), \] where \( x(t) \) and \( y(t) \) are the input and output respectively. Its impulse response is

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

Two discrete-time linear time-invariant systems with impulse responses \(h_1[n] = \delta[n-1] + \delta[n+1]\) and \(h_2[n] = \delta[n] + \delta[n-1]\) are connected in cascade. The impulse response of the cascaded system is