Digital signal processing circuits, systems, and method implementing approximations for logarithm and inverse logarithm

摘要

A digital signal system (100) for determining an approximate logarithm of a value of x having a base b. The approximate logarithm includes an integer portion (i) and a decimal portion (f). The system comprises an input (12) for receiving a signal, and circuitry (18) for measuring an attribute of the signal. The attribute relates at least in part the value of x. The system further comprises circuitry (104) for identifying a bounded region within which x falls. The bounded region is one of a plurality of bounded regions, where each of the plurality of bounded regions corresponds to a different value of an integer n and is bounded on a lower side by bn and on a higher side by bn+1. Additionally, the identified bounded region identifies the integer portion of the approximate logarithm. The system further comprises circuitry (106, 108) for determining the decimal portion of the approximate logarithm by mapping a portion of x to a point along a curve representing an approximation of a portion of an actual logarithm value of x.