Trignometric Function Generator Implementation on FPGA

Abstract

CORDIC is an acronym for COrdinate Rotation Digital Computer. It is a class of shiftadd algorithms for rotating vectors in a plane, which is usually used for the calculation of trigonometric functions, multiplication, division and conversion between binary and mixed radix number systems of DSP applications, such as Fourier Transform. The Jack E. Volder's CORDIC algorithm is derived from the general equations for vector rotation. A new algorithm was presented by R. E. Fowkes[23] which significantly reduces the minimum amount of logic required to calculate sine, cosine, and square root. It is derived from an old method for computing certain inverse functions which was once considered for use in software, but then abandoned because of efficiency concerns. However, when reversed and combined with a restoring square root algorithm, a unique new design emerges which performs trigonometric calculations without the use of pre-stored constants or any internal operation more complex than binary subtraction. The algorithm has been implemented in FPGA using VHDL and is found to be accurate with an error of -2.9% to 2% for square root, an error of -1.4% to .19% for cosine and an error of -6.5% to 1.9% for sine. The implementation of this algorithm requires less hardware than the comparable CORDIC algorithm. This thesis consists of introduction to both the algorithms. The description of the algorithm and finally a comparative study of the algorithm is been presented in this thesis. The results constitute simulation of VHDL codes of different modules and their synthesis in Xilinx Foundation Series ISE-6.