A Note on Stable, Physically Realizable, Linear, Time Invariant Systems

A time invariant system is said to be physically realizable if its unit impulse response is zero for . It is often assumed, in treatments of physical realizability, that the Fourier transform of is square integrable . Some use is then made of the regularity of the transform, for real frequencies, to derive further properties of the transform. The condition that the system be stable leads to a different assumption, that be integrable (is ); this implies only uniform continuity of the transform for real frequencies. Physically realizable, stable systems are discussed in this note, and several necessary, and a few sufficient, conditions on the Fourier transform of are summarized. In particular, the behavior of the transform for complex frequencies, the Bode relations, and the Paley-Wiener criterion, are reviewed.