On the recovery of the time average of continuous and discrete time functions from their Laplace and z‐transforms
On the recovery of the time average of continuous and discrete time functions from their Laplace and z‐transforms
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关于从拉普拉斯和 z 变换中恢复连续和离散时间函数的时间平均值
DOI：
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发表时间：
2011
影响因子：
2.3
通讯作者：
Shmuel Y. Miller
中科院分区：
文献类型：
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作者：
E. Gluskin;Shmuel Y. Miller
确定连续函数或离散时间序列的时间平均值对于物理和工程中的各种问题都很重要，而拉普拉斯和z变换的广义终值定理，与在无穷远处没有极限但具有明确定义的平均值的函数和序列相关，可以在此确定中非常有用。在本文中，我们完成了这些定理的证明，并将它们推广到更一般的时间函数和序列。除了正式的证明，一些简单的例子和启发式和教学的评论的物理性质的限制过程定义的平均。版权所有© 2012约翰威利父子有限公司.
The determination of the time averages of continuous functions or discrete time sequences is important for various problems in physics and engineering, and the generalized final‐value theorems of the Laplace and z‐transforms, relevant to functions and sequences not having a limit at infinity, but having a well‐defined average, can be very helpful in this determination. In the present contribution, we complete the proofs of these theorems and extend them to more general time functions and sequences. Besides formal proofs, some simple examples and heuristic and pedagogical comments on the physical nature of the limiting processes defining the averaging are given. Copyright © 2012 John Wiley & Sons, Ltd.