An input x(t) = exp( -2t) u(t) + $$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is

A continuous time LTI system is described by $${{{d^2}y(t)} \over {d{t^2}}} + 4{{dy(t)} \over {dt}} + 3y(t)\, = 2{{dx(t)} \over {dt}} + 4x(t)$$.

Assuming zero initial conditions, the response y(t) of the above system for the input x(t) = $${e^{ - 2t}}$$ u(t) is given by

Consider a system whose input x and output y are related by the equation $$$y(t) = \int\limits_{ - \infty }^\infty {x(t - \tau )\,h(2\tau )\,d\tau } $$$

Where h(t) is shown in the graph.

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.
Causal: The system is casual.
LP: The system is low pass.
LTI: The system is linear and time- invariant.

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero at s = - 1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is