论文标题
数据近似与时频不变系统
Data approximation with time-frequency invariant systems
论文作者
论文摘要
在本文中，我们证明了最近似于给定有限数据的时频空间的存在。在这里，最好的近似值是在最小平方的意义上，在所有时频的空间中，只有规定的发电机数量。我们提供了一个公式，可以从数据中构造发生器，并提供近似的确切误差。该设置位于第二个可数LCA组上定义的平方集成函数的空间，我们将Zak变换用作主要工具。
In this paper we prove the existence of a time-frequency space that best approximates a given finite set of data. Here best approximation is in the least square sense, among all time-frequency spaces with no more than a prescribed number of generators. We provide a formula to construct the generators from the data and give the exact error of approximation. The setting is in the space of square integrable functions defined on a second countable LCA group and we use the Zak transform as the main tool.
