Behavior of Attenuation for Systems Having Monotonic Step and Impulse Responses

If a system has a monotonically increasing step response, the magnitude of the system function cannot attentuate too rapidly. This well-known fact is given greater precision in this paper by the establishment of a set of lower bounds on the magnitude function, these results being an improvement over some previously published ones. More precisely, if at some the value of is known, thereby determining through , then lower bounds on are determined for and for > 1. Stronger results are then established for system functions whose impulse responses are monotonically decreasing. The strengthening of these results resides in the fact that assumes continuous values with gt; 1 rather than the discrete integer values of the previous case.