Causal, stable and homogeneous formulas for acoustic and ultrasonic propagation through atmosphere

This is the authors' abstract. We don't add key points for this paper.

This paper addresses the propagation of acoustics or ultrasonics waves through atmosphere and the causality property. The physicists community seems to agree with the following sentence:… empirical observation indicates that such systems are indeed causal even though the transfer function may not be a causal transform.We explain that the complex gain is not causal when not properly chosen, and that this issue can be addressed.