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

本研究计划旨在发展一种新的信号处理理论和方法，通过现代采样数据控制理论优化模拟性能。这里的中心问题是超出所谓的奈奎斯特频率的重建/恢复。在由香农发起的传统方法中，人们采取的观点是，在奈奎斯特频率之外没有信息内容可用。这种观点现在是无处不在的，并且毫无疑问地被信号处理的各个方面所接受。目前的做法质疑这种假设的有效性。事实上，根据现代采样数据控制理论的成就，如果可以假设总体频率衰减特性，则可以内插样本间行为。这与Shannon方法形成了鲜明的对比。本研究成功地导出了一种滤波器，该滤波器产生了次优的模拟性能，并且已经保证它在声音处理中给出了上级结果。这一点在一个新设计的采用DSP的DA转换器中也得到了保证。该DA转换器的性能优于目前市场上的高端CD播放器。我们还获得了一种新的声音压缩算法和一种新的声音恢复算法;后者现在已被几个商业用途所采用。我们还表明，新的方法是适用于图像处理，并确实提高了图像质量。更实际的方面是未来研究的主题。

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.