Information granulation and signal quantization

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 fund amental issues of information granulation. The paper elaborates on and cont rasts 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 aware ness about the performance of the quantization process and helps increase i ts quality by defining additional elements of the codebook and specifying t heir range of applicability. We show how different information granules con tribute to the performance of signal quantification. The rob of clustering techniques giving rise to information granules is also analyzed. Some perti nent theoretical results are derived. It is shown that fuzzy sets defined i n terms of piecewise linear membership Junctions with 1/2 overlap between a ny two adjacent terms of the codebook give rise to the effect of lossless q uantization. The study addresses both scalar and multivariable quantization . Numerical studies are included to help illustrate the quantization mechan isms earned out in the setting of granular computing.