Sampled-Data Control & Digital Signal Processing

本研究项目旨在将主要研究人员发展的现代函数论方法应用于采样数据控制系统，并将其应用于数字信号处理。这里的重点是基于被称为提升的新概念的设计模型中内置的样本间行为，因此与经典的处理方式有很大的不同。特别是，与数字信号处理中传统的离散时间域技术相比，它为处理数字滤波器的连续时间行为提供了一个舒适的平台。频域分析/综合法，2.频率响应的近似计算方法3。采用采样数据控制的滤波器综合框架4。扩展到多速率滤波器组5。在研究期间，我们成功地得到了以下结果：1.近似频率响应对原始采样数据系统的收敛证明。单速率信号重构问题的约化公式。其扩展到多速率滤波器组4。在最优DA转换器设计中的应用。应用于重复控制方案6。实现为一个CAD包。还获得了一个与小波连接的有希望的迹象。目前的研究与这一主题的相互作用无疑是未来最有趣和最富有成效的目标。

The present research project intends to advance and apply the modern function theoretic approach, developed by the principal investigator, to sampled-data control systems and apply it to digital signal processing. The emphasis here is upon the built-in intersample behavior in the design model based on the new notion called lifting, thereby differing greatly from the classical treatment. In particular, it gives a comfortable platform for dealing with continuous-time behavior of digital filters in contrast to the conventional discrete-time domain techniques in digital signal processing.It aims at advancing1. frequency domain analysis/synthesis methods,2. approximate methods for computing the frequency response3. framework for filter synthesis with sampled-data control4. extension to multirate filter banks5. application to various concrete situations.During the research term, we have successfully obtained the following results :1. Convergence proof of approximate frequency responses to that of the original sampled-data system2. Reduction formula for single-rate signal reconstruction problem3. Its extension to multirate filter banks4. Application to the design of optimal DA converters5. Application to the repetitive control scheme6. implementation as a CAD package.A promising sign of connection with wavelets has also been obtained. The interplay of the present research with this theme is undoubtedly the most interesting and fruitful target for the future.