General Theory of Digital Signal Processing via-Sampled Data Control Theory and Its Applications

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This research project intends to develop a new theory and method of signal processing that optimize analog performance via modern sampled-data control theory. The central issue here is the reconstruction/restoration beyond the so-called Nyquist frequency. In the conventional approach, initiated by Shannon, one takes the viewpoint that no information content is available beyond the Nyquist frequency. This viewpoint is now ubiquitous, and accepted without a doubt in all aspects of signal processing. The present approach questions the validity of such an assumption. Indeed, according to the accomplishments of modern sampled-data control theory, it is possible to interpolate the intersample behavior, if one can assume an overall frequency decay characteristic. This is in marked contrast to the Shannon approach.The present research has successfully derived a filter that gives rise to a suboptimal analog performance, and it has been guaranteed that it gives a superior result in sound processing. This has been also assured in a newly designed DA converter using a DSP. This DA converter has shown to outperform the current high-end CD players available in the market.We have also obtained a new sound compression algorithm and a new sound restoration algorithm ; the latter is now adopted in a several commercial use. We have also shown that the new method is applicable to image processing, and indeed improves image quality. More practical aspects are themes for future study.