Comparison of Fixed-Point Arithmetic Errors for the FPGA-Based CRAIMOT Basis Function Generators

This paper describes the mean square error (MSE) of basis function (BF) caused by the quantization of sine/cosine values. MSEs for all CRAIMOT BFs are equal. Additionally, MSEs are estimated for random signals synthesized by a limited number of weighted CRAIMOT BFs (partial sum). Maximal and minimal MSEs are given in dependence on the wordlength of sine/cosine former and the number of BFs used for synthesis. Synthesis error is independent of the number of BFs, practically constant. Errors are compared for two versions of FPGA implemented BF generator and synthesizer. Versions of mentioned devices differ by sine/cosine former blocks implemented using CORDIC and optimal linear interpolation algorithms. A CORDIC former ensures approximately twice better accuracy. A preliminary simulation has been conducted and it has proved the existence of optimal angles (optimal transforms) from the implementation point of view.