Signal synthesis in the presence of an inconsistent set of constraints
Signal synthesis in the presence of an inconsistent set of constraints
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DOI：
10.1109/tcs.1985.1085777
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发表时间：
1985-07
期刊：
影响因子：
--
通讯作者：
M. Goldburg;R. Marks
中科院分区：
文献类型：
--
作者：
M. Goldburg;R. Marks
在本文中，我们提出了一种新的技术，在存在不一致的约束条件下的信号合成。这种技术代表了一类综合问题的一般最小范数解，其中：所需信号可以被表征为某个希尔伯特空间的元素; N个设计约束中的每一个都在该空间中生成一个闭凸集;并且这N个凸集生成或可以被分解为两个不相交的闭凸集，使得这两个集合中的至少一个是有界的。该合成技术采用交替最近点映射到Hilbert空间的闭凸子集上，并且可以被看作是D. Youla的“凸投影法”--它解决了与设计约束相对应的N个闭凸集具有非空交集的情况。第一节提供了一个综合问题和它的解决方案的一般性介绍。第二节包含的解决方案的技术的数学理由，而第三节提出了一个例子，合成的数据窗口的光谱估计。在第四节中，我们讨论了信号合成领域内这种技术的潜在扩展，以及更一般的约束优化问题。
In this paper, we present a novel technique for signal synthesis in the presence of an inconsistent set of constraints. This technique represents a general, minimum norm, solution to the class of synthesis problems in which: the desired signal may be characterized as being an element of some Hilbert Space; each of the N design constraints generates a closed convex set in that space; and those N convex sets generate, or may be resolved into, two disjoint closed convex sets, such that at least one of the two sets is bounded. The synthesis technique employs alternating nearest point maps onto closed convex subsets of a Hilbert Space, and may be viewed as an extension of D. Youla's "Method of Convex Projections"--which addresses the case in which the N closed convex sets, corresponding to the design constraints, possess a nonempty intersection. Section I provides a general introduction to the synthesis problem and to its solution. Section II contains the mathematical justification for the solution technique, while Section III presents an example of the synthesis of a data window for spectral estimation. In Section IV, we discuss potential extensions of this technique within the area of signal synthesis, as well as to the more general class of constrained optimization problems.