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In this thesis, we present a new method for designing multirate signalprocessing and digital communication systems via sampled-data H-infinitycontrol theory. The difference between our method and conventional ones is inthe signal spaces. Conventional designs are executed in the discrete-timedomain, while our design takes account of both the discrete-time and thecontinuous-time signals. Namely, our method can take account of thecharacteristic of the original analog signal and the influence of the A/D andD/A conversion. While the conventional method often indicates that an idealdigital low-pass filter is preferred, we show that the optimal solution neednot be an ideal low-pass when the original analog signal is not completelyband-limited. This fact can not be recognized only in the discrete-time domain.Moreover, we consider quantization effects. We discuss the stability and theperformance of quantized sampled-data control systems. We justify H-infinitycontrol to reduce distortion caused by the quantizer. Then we apply it todifferential pulse code modulation. While the conventional Delta modulator isnot optimal and besides not stable, our modulator is stable and optimal withrespect to the H-infinity-norm. We also give an LMI (Linear Matrix Inequality)solution to the optimal H-infinity approximation of IIR (Infinite ImpulseResponse) filters via FIR (Finite Impulse Response) filters. A comparison withthe Nehari shuffle is made with a numerical example, and it is observed thatthe LMI solution generally performs better. Another numerical study alsoindicates that there is a trade-off between the pass-band and stop-bandapproximation characteristics.

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