From Sampled-data Control to Signal Processing: Beyond the Shannon Paradigm

Abstract

There has been remarkable progress in sampled-data control theory in the last two decades. The main achievement here is that there exists a digital (discrete-time) control law that takes the intersample behavior into account and makes the overall analog (continuous-time) performance optimal, in the sense of H-infinity norm. This naturally suggests its application to digital signal processing where the same hybrid nature of analog and digital is always prevalent. A crucial observation here is that the perfect band-limiting hypothesis, widely accepted in signal processing, is often inadequate for many practical situations. In practice, the original analog signals (sounds, images, etc.) are neither fully band-limited nor even close to be band-limited in the current processing standards. The problem is to interpolate high-frequency components beyond the so-called Nyquist frequency, and this is nothing but the intersample signals discarded through sampling. Assuming a natural signal generator model, sampled-data control theory provides an optimal platform for such problems. This new method has been implemented to a custom LSI chips by SANYO corporation, and has made success of producing over 12 million chips. This talk provides a new problem formulation, design procedure, and various applications in sound processing/compression and image processing.