Multirate Digital Signal Processing via Sampled-Data H-infinity Optimization

Abstract

In this thesis, we present a new method for designing multirate signal processing and digital communication systems via sampled-data H ∞ control theory. The difference between our method and conventional ones is in the signal spaces. Conventional designs are executed in the discrete-time domain, while our design takes account of both the discrete-time and the continuoustime signals. Namely, our method can take account of the characteristic of the original analog signal and the influence of the A/D and D/A conversion. While the conventional method often indicates that an ideal digital low-pass filter is preferred, we show that the optimal solution need not be an ideal low-pass when the original analog signal is not completely band-limited. This fact can not be recognized only in the discrete-time domain. Moreover, we consider quantization effects. We discuss the stability and the performance of quantized sampled-data control systems. We justify H ∞ control to reduce distortion caused by the quantizer. Then we apply it to differential pulse code modulation. While the conventional ∆ modulator is not optimal and besides not stable, our modulator is stable and optimal with respect to the H ∞ -norm. We also give an LMI (Linear Matrix Inequality) solution to the optimal H ∞ approximation of IIR (Infinite Impulse Response) filters via FIR (Finite Impulse Response) filters. A comparison with the Nehari shuffle is made with a numerical example, and it is observed that the LMI solution generally performs better. Another numerical study also indicates that there is a trade-off between the pass-band and stop-band approximation characteristics.I would like to express my sincere gratitude to everyone who helped me and contributed in various ways toward completion of this work.First of all, I am most grateful to my supervisor Professor Yutaka Yamamoto. Since I entered the Graduate School of Kyoto University, he has constantly guided me in every respect of science and technology. Without this knowledge he has endowed me, it is unthinkable that I could proceed this far toward the completion of this thesis. He also taught me fundamental knowledge on sampled-data control and signal processing on which this thesis is based. His strong leadership and ideas have been a constant source of encouragement and have had a definite influence on this work. Without his supervision, this thesis would not exist today.I would also like to thank Dr. Hisaya Fujioka for his helpful discussions and support in my research, in particular, those on sampled-data control. His warm encouragement was also great help to completing this thesis.My gratitude should be extended to Dr. Yuji Wakasa for his valuable advice. In particular, his advice on convex optimization was very valuable to my research.I would thank Mr. Kenji Kashima, Mr. Shinichiro Ashida, and current and past members of the intelligent and control systems laboratory for their academic stimulation and dairy friendship.Special thanks are addressed toward my parents for their deep understanding and...