Reciprocity Inequalities, Coherence Time and Bandwidth in Signal Analysis and Optics (Classic Reprint) - Softcover

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Excerpt from Reciprocity Inequalities, Coherence Time and Bandwidth in Signal Analysis and Optics

As a preliminary, Gabor's proof is completed and it is shown that the quantity At defined by him (to be denoted A't here) may be interpreted as the normalized r.m.s. Of the squared amplitude of the envelope belonging to the real signal. Moreover, it will be shown that if A't exists, it is equal to the normalized r.m.s. Width [fit of the square of the real signal itself. However, the require ment of the existence of Adt is found to be a rather strong one. For example, if the real signal V(t) is zero outside a finite interval -t f t 5 T, then At exists but A't does not exist unless the average value of the signal is zero, or what amounts to the same thing, unless the signal has no spectral components of zero frequency. This condition is satisfied in the application discussed in this paper, but the need for imposing it raises doubts about the validity of the inequality for an arbitrary real signal when 7 and Av are redefined in accordance with our intuitive notion of these quantities.

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