Physical Bounds on the Time-Domain Response of a Linear Time-Invariant System

Early-time and late-time physical bounds on the causal response of a linear time-invariant and stable system are derived through analytic properties of its one-sided Laplace-transform counterpart. The analysis relies merely on Cauchy's theorem and integral formula and is valid for systems satisfying some definite sign requirements on its frequency response. Illustrative numerical examples demonstrating the validity of time-domain bounds are presented.