Study of numerical analysis via control theory

本研究旨在发展一种新的解决方案，通过现代采样控制理论获得的滤波器。由于采样数据控制理论通过离散时间模型处理连续时间信号，这种方法预计将开发一个新的视野，也鉴于在声音和图像处理的高度成功的结果。然而，虽然确保是有效的线性时不变系统，新的计划被发现是无效的非线性或刚性系统。这被认为是由于所设计的滤波器所基于的系统特性的时不变性质，因此这些滤波器对于计算瞬态不是那么有效。这导致了猜想，人们应该着手发展时变滤波器。然而，作为副产品，已经发现这样的时不变滤波器可以有效地通过数字处理来减少相位失真。这样的特性在声音和图像处理中是有用的，并且期望在未来变得更有效。

This research intended to develop a new solution scheme via filters obtained by modern sampled-data control theory. Since sampled-data control theory processes continuous-time signals via discrete-time models, this approach is expected to develop a new horizon, also in view of the highly successful outcomes in sound and image processing. Nonetheless, while ensured to be effective for linear-time invariant systems, the new scheme was found not to be effective for nonlinear or stiff systems. This is presumed to be due to the time-invariant nature of the system characteristic on which the designed filters are based, and hence those filters are not so effective for computing transients. This leads to the conjecture that one should proceed to a development of time-varying filters. As a byproduct, however, it has been found that such time-invariant filters can be effective in reducing phase distortions by digital processing. Such a characteristic is useful in sound and image processing, and expected to become more effective in the future.