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In a communication scheme, there exist points at the transmitter and at thereceiver where the wave is reduced to a finite set of functions of time whichdescribe amplitudes and phases. For instance, the information is summarized inelectrical cables which preceed or follow antennas. In many cases, a randompropagation time is sufficient to explain changes induced by the medium. Inthis paper we study models based on stable probability laws which explain powerspectra due to propagation of different kinds of waves in different media, forinstance, acoustics in quiet or turbulent atmosphere, ultrasonics in liquids ortissues, or electromagnetic waves in free space or in cables. Physical examplesshow that a sub-class of probability laws appears in accordance with thecausality property of linear filters.

Stable probability laws modeling random propagation times of waves crossing different media