Sorter-Based Arithmetic Circuits for Sigma-Delta Domain Signal Processing—Part I: Addition, Approximate Transcendental Functions, and Log-Domain Operations

We construct arithmetic modules for signal processing with sigma-delta modulated signal form which has advantage in signal quality over other pulsed signal forms. In the first part of this paper, adders and exponential function modules are presented first and secondly. By utilizing the two modules, several transcendental functions including hyperbolic and logarithmic functions are constructed. The exponential functions and logarithmic functions provide log-domain arithmetic operations including multiplication, division, and power functions. Only two bit-manipulations, bit-permutation with sorting networks and bit-reversal with NOT gates, have built up all the arithmetic operations on any form of sigma-delta modulated signals. These modules, together with algebraic functions to be presented in the second part of this paper, organize an extensive module library for the sigma-delta domain signal processing.