Efficient Data Representations for Signal Processing and Control: "Making Most of a Little"

In order that signals can be stored, transmitted or processed it is necessary that they first be converted into digital form. This, in turn, raises the problem of how to digitize data so as to achieve the best trade-off between data load and performance, i.e., "how to make the most out of a little". Two issues are involved in this problem, namely temporal quantization (i.e., sampling) and spatial quantization. These two problems have traditionally been addressed separately. Indeed, there exists substantial literature dealing with the temporal quantization problem, covering both band-limited and non-band-limited signals. The usual underlying paradigm is that of an analysis filter, followed by a sampler, followed by a reconstruction filter. Various parts of this architecture can be optimized once other parts have been specified. On the other hand, spatial quantization has been studied extensively for a given sampling strategy, particularly in the framework of sigma delta conversion. Finally, it is also possible to formulate the joint design problem for sampling and spatial quantization. This typically leads to enhanced performance compared to that achievable by considering the two aspects separately. This paper will survey the general area of sampling and quantization and analyze methods for achieving efficient data representations for signal processing and control applications. We will show how, on the one hand, contemporary control theory can contribute to the design of sampling and quantization systems and, on the other hand, how these systems impact on the performance of modern feedback control systems.