On The Minimum-length Property Of One-sided Signals

TLDR: In this paper, the authors introduced the concept of signal duration and signal length as two different concepts, and proposed an objective signal length measurement metric based on the amplitude and phase spectrum.

Abstract: Apart from a visual inspection, the length property of a signal is mostly judged by its amplitude spectrum (e.g., bandwidth or “roughness” of the spectrum). However, due to the important influence of the phase spectrum. a sensible yardstick for signal length should consider both amplitude and phase. In addition, a complete investigation should also include evaluation of the length of the (partly) deconvolved signal. In this paper, signal duration and signal length are introduced as two different concepts. Unlike signal duration, giving the minimum time interval outside of which the signal equals zero, signal length gives some information as to how the signal energy is distributed within this interval. An objective yardstick for signal length is proposed, and it is shown how signal length depends on both the amplitude and phase spectrum. The minimum‐length signal is introduced and it is shown that for one‐sided signals the minimum signal‐length property implies the minimum‐phase property and vice‐versa. Th...