Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ – \infty }^\infty {x\left( {t – \tau } \right)} h\left( {2\tau } \right)d\tau $$ 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 causal. LP : The system is low pass. LTI: The system is linear and time-invariant.

The correct answer is B. BIBO, LTI.

The system is BIBO stable because the integral of $|h(t)|$ is finite. The system is causal because the output depends only on the past and present inputs. The system is linear because the output is a linear combination of the inputs. The system is time-invariant because the output is the same for any input that is delayed by a constant time.

The system is not low pass because it does not pass low frequencies without attenuation. The graph of $h(t)$ shows that the system attenuates low frequencies.