BIT SERIAL CORDIC DDFS

Abstract

CORDIC is an acronym for Coordinate Rotation Digital Computer. It is a class of shift adds 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. The CORDIC algorithm has become a widely used approach to elementary function evaluation when the silicon area is a primary constraint. The implementation of CORDIC algorithm requires less complex hardware than the conventional method. In digital communication, the straightforward evaluation of the cited functions is important, numerous matrix based adaptive signal processing algorithms require the solution of systems of linear equations, the computation of eigen values, eigenvectors or singular values. All these tasks can be efficiently implemented using processing elements performing vector rotations. The (CORDIC) offers the opportunity to calculate all the desired functions in a rather simple and elegant way. Due to the simplicity of the involved operations the CORDIC algorithm is very well suited for VLSI implementation. Verilog coding and simulation of bit serial CORDIC algorithm for sine and cosine, the comparison of resultant implementations and the specifics of the FPGA implementation has been discussed. In this thesis, the CORDIC algorithm has been implemented in XILINX Spartan 3E FPGA kit using Verilog and is found to be accurate. It also contains bit serial implementation of CORDIC algorithm on the same FPGA kit which is actually the problem statement. Due to the high speed, low cost and greater flexibility offered by FPGAs over DSP processors the FPGA based computing is becoming the heart of all digital signal processing systems of modern era. Moreover the generation of test bench by Xilinx ISE 9.2i verifies the results.