Sampled-Data Control & Digital Signal Processing

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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.