Sampled-Data Control & Digital Signal Processing

本研究项目旨在推进和应用现代函数理论的方法，开发的主要研究者，采样数据控制系统，并将其应用于数字信号处理。这里的重点是基于称为提升的新概念的设计模型中的内置样本间行为，从而与经典处理方法有很大不同。特别是，它提供了一个舒适的平台，用于处理连续时间的数字滤波器的行为相比，传统的离散时域技术在数字信号处理。频域分析/综合方法; 2.计算频率响应的近似方法3.具有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，我们成功地取得了以下成果：1。近似频率响应对原始采样数据系统频率响应的收敛性证明2.单速率信号重建问题的简化公式3.其扩展到多速率滤波器组4.应用于最佳DA转换器的设计5.应用于重复控制方案6.实现作为一个CAD软件包。一个有前途的迹象连接小波也已获得。目前的研究与这一主题的相互作用无疑是未来最有趣和富有成效的目标。

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.