A simple high-performance sine/cosine reference generator

This paper describes a simple sine/cosine generator which is designed to provide a rate-signal demodulation reference for a gyroscope in a tactical-grade inertial-reference system. The algorithm for computing the parameters is also described. The design driver is high performance at low cost/complexity. Only 3 multiplies and 5 adds operate on each input sample. The input to the sine/cosine generator is phase angle which is provided by a source to which we have no internal access. By dividing the 360-degree input-phase cycle into 5 unequal-length segments and constraining the end-points, a surprisingly good fit can be found using a Chebychev approximation to compute 5 stored coefficients (3 are used together to form one approximation; the other 2 are used together to form a second approximation). The Remez-exchange algorithm is used to form the Chebychev fit, and an LMS algorithm (which is imbedded into the same program) optimizes the endpoints. The Remez and LMS update cycles are common; seldom are more than 3 or 4 iterations required to obtain a satisfactory design solution