Generalized CORDIC for digital signal processing

Many fast signal processing algorithms are based on a geometric framework and efficient implementations of these algorithms often require the computation of elementary functions involving such operations as vector rotations and exponentials. The CORDIC (COordinate Rotation Digital Computer) algorithms are the natural candidates for these elementary operations and they lead to novel realizations in many promising algorithms such as the square-root normalized ladder algorithms. FFT and several well-known matrix algorithms for signal processing. The development of algorithms involving nonstationary processes and the limiting constraints of VLSI motivate the extension of the CORDIC concept in other directions. It can be applied not only to one-parameter groups but to other Lie groups as well, i.e., higher dimensional manifolds, leading to generalized CORDIC algorithms. The computation of special functions is some of the potential benefits. Several such generalizations will be discussed.