Discrete Orthogonal Transforms Using Cellular Automata
Thomas Zheng University of California, San Diego
Transforms are important tools for scientists and engineers studying complexity. The author postulates that complexity can be manipulated through transforms, i.e. reduced or multiplied. In this topic, one particular type of transform, Discrete Orthogonal Transform (DOT), is discussed. In particular, the author draws the systematic connection between DOT and CAs. Starting by looking at the Fast Fourier Transform (FFT) algorithm, the author demonstrates that many other Discrete Orthongonal Transforms can be implemented by a two-stage cellular automata consisting of an additive CA and a reversible CA. Extensions to Generalized Transform (GT) using Cellular Automata will also be discussed.