Successive Approximation Algorithm for Complex Number Magnitude and Argument Computation

Abstract

Determination of complex number modulus and argument is commonly encountered task in digital signal processing. According to definition, this task requires evaluation of square root and inverse tangent functions. When computing hardware resources are limited, e.g. in real-time applications, an approximation by basic arithmetic and logical operations are of interest. We propose method for modulus approximation that uses addition, scaling and comparison, and provides also argument information. At each additional level of our algorithm, modulus approximation error decreases by factor of 4 and argument error by factor of 8.