Memory reduction in look-up tables for fast symmetric function generators

This paper describes a new hardware technique, providing high-resolution trigonometric functions sine and cosine reading for an angle θ from a significantly reduced size lookup table (LUT). The method takes advantage of the symmetries of these trigonometric functions around several axis and the fact that the cosine function can be derived by shifting the sine function by π/2 backward. This shifting is achieved using a very fast hardware technique. A linear interpolation technique can be used if a further reduction in needed memory is desired. Experimental results are given. The described system can be used in precision analog symmetric function generators, in robotic arm controllers, in position control systems etc