  In this thesis, we present a new method for designing multirate signal
processing and digital communication systems via sampled-data H-infinity
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
continuous-time 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-infinity
control to reduce distortion caused by the quantizer. Then we apply it to
differential pulse code modulation. While the conventional Delta modulator is
not optimal and besides not stable, our modulator is stable and optimal with
respect to the H-infinity-norm. We also give an LMI (Linear Matrix Inequality)
solution to the optimal H-infinity 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.
