A signal \(x(t) = \sin c(α t)\), where α is a real constant, is the input to a Linear Time-Invariant system whose impulse response is \(h(t) = \sin c(β t)\), where β is a real constant. If min (α, β) denotes the minimum of α and β and similarly, max (α, β) denotes the maximum of α and β, and K is a constant, which one of the following statements is true about the (here, \(\sin c\left( x \right) = \frac{{\sin \left( {\pi x} \right)}}{{\pi x}}\)) output of the system?

• A. It will be of the form \(K\sin c\left( {γ t} \right)\) where γ = min (α, β)
• B. It will be of the form \(K\sin c\left( {γ t} \right)\) where γ = max (α, β)
• C. It will be of the form \(K\sin c\left( {\alpha t} \right)\)
• D. It cannot be a \(\sin c\) type of signal