Information granulation and signal quantization

Abstract

Shows that signal quantization can be conveniently captured and quantified in the language of information granules. Optimal codebooks exploited in any signal quantization (discretization) lend themselves to the underlying fundamental issues of information granulation. The paper elaborates on and contrasts between various forms of information granulation such as set theory, shadowed sets, and fuzzy sets. It is revealed that a set‐based codebook can be easily enhanced by the use of the shadowed sets. This also raises awareness about the performance of the quantization process and helps increase its quality by defining additional elements of the codebook and specifying their range of applicability. We show how different information granules contribute to the performance of signal quantification. The role of clustering techniques giving rise to information granules is also analyzed. Some pertinent theoretical results are derived. It is shown that fuzzy sets defined in terms of piecewise linear membership functions with 1/2 overlap between any two adjacent terms of the codebook give rise to the effect of lossless quantization. The study addresses both scalar and multivariable quantization. Numerical studies are included to help illustrate the quantization mechanisms carried out in the setting of granular computing.