The \(\beta \alpha \)-encoders for robust A/D conversion (Q1038727)

In digital systems or communications we have as an encoding A/D (source encoder or analog to digital converter) the binary quantization system. In this paper, a mathematical algorithm of the \(\beta\)-encoder or \(\beta\)-expander is analysed and a robust system to the field is given. Also the paper introduces a more advanced system, the so called \(\beta\alpha\)-encoder which allows, as it is proven, that it gives more flexibility, challenge and robustness, so it is more interesting and dynamic. In this given algorithm, some constants are examined such as bounds (upper bound), the \(\beta\alpha\)-multiplication and ergodicity.