Algorithm and two efficient implementations for complex multiplier

Complex number operations are the backbones for many digital signal processing (DSP) algorithms and several other scientific applications. In this paper, a complex multiplication algorithm and two of its realizations are provided. The first realization is a direct implementation of the algorithm. The second realization is complex but more efficient in both hardware and time. This realization processes information in a pipeline fashion thus it is valuable for applications with long sequences of complex operations. The hardware and time saving of the second realization over the simple one is approximately forty percent. Furthermore, the two proposed implementations could be used to perform cyclic convolutions of two point sequences just by negating one of its inputs.