The efficient implementation of complex number arithmetic

Complex number arithmetic computation is a key arithmetic feature in modern digital communication, radar systems and optical systems. These applications require efficient representation and manipulation of complex numbers together with real numbers. To represent a complex number other than radix-(2), several representations such as radix-(2j), radix-(-j+l), etc, have been proposed. Multiplication is an essential operation for high-speed hardware implementation of complex number computations. It can be used to compare the complexity of complex number arithmetic using different complex radices. In this paper, different complex radices are investigated and compared. We rind that these complex radices have no advantage in hardware implementations. Based upon our new proposed complex number multiplier, we conclude that traditional radix(2) redundant binary numbers are most efficiently used to implement complex-number multiplication.