A single modulus complex ALU for signal processing

Fast complex arithmetic is essential to a wide class of real-time digital transform and filter operations. Traditional methods require a multiplicity of real multiplies and adds be performed on each complex product call. Recently, a new modular (residue) mathematical system has been proposed which more than halves this count. The system developed in this paper overcomes many of the classical weaknesses of a general L-moduli modular system. Such a system is architected, its hardware implementation developed, and complexity-performance metrics analyzed. Both general purpose and array processing forms are advanced and discussed. Special operations, such as complex magnitude squared calculations, are shown to have a particularly efficient implementation in this system. Last, several DSP applications of the developed complex ALU are motivated and experimentally studied.