Quantization issues in signal processing and control system design

Many interesting design problems encountered in signal processing and control turn out to depend on a set of decision variables that can only take a finite number of values, i.e., they are quantized. For example, in power distribution networks there are only a finite number (typically small) of generators and possible transmission options. Other examples abound in many fields, e.g., on-off control problems, quantization of audio signals for CD-production, filter banks for audio and video compression, switch-mode power supplies used, e.g., in laptop computers, and so on. All of these problems share the common feature that the decision space is quantized. The associated design problems require special attention since they are inherently "nonconvex" in a technical sense. This paper gives an overview of quantization issues in signal processing and control and points to recent research aimed at providing designs that can be utilized in practice