Self-stabilizing, portable and efficient computer arithmetic using mappings of D Scale points

摘要

A method and apparatus for signal and noise processing employs a D Scale, which assigns the results of arithmetic operations to a set of values of controlled density and value. The signal processor has two components, a set of mappings from pairs of points in a D Scale into a point in a D Scale, and a map of measured values, into D Scale points. A tight variance of the resolution is achieved by using prime sub-scales to fill in the D Scale. Fewer sample points attain the same mean resolution, with a tight variance, as a high uniform sampling rate. The invention bounds the round-off errors of sequential calculations, and decouples actual noise from the artifact created by calculation round-off errors. The invention provides a Discrete Fourier Transform (DFT) of a signal or image as an example of a continuous-to-discrete transformation.