CORDIC algorithm and it’s applications in DSP

Abstract

OBJECTIVE: The digital signal processing landscape has long been dominated by the microprocessors with enhancements such as single cycle multiply-accumulate instructions and special addressing modes. While these processors are low cost and offer extreme flexibility, they are often not fast enough for truly demanding DSP tasks. The advent of reconfigurable logic computers permits the higher speeds of dedicated hardware solutions at costs that are competitive with the traditional software approach. Unfortunately algorithms optimized for these microprocessors based systems do not map well into hardware. While hardware efficient solutions often exist, the dominance of the software systems has kept these solutions out of the spotlight. Among these hardware- efficient algorithms is a class of iterative solutions for trigonometric and other transcendental functions that use only shifts and adds to perform. The trigonometric functions are based on vector rotations, while other functions such as square root are implemented using an incremental expression of the desired function. The trigonometric algorithm is called CORDIC an acronym for Coordinate Rotation Digital Computer. The incremental functions are performed with a very simple extension to the hardware architecture and while not CORDIC in the strict sense, are often included because of the close similarity. The CORDIC algorithms generally produce one additional bit of accuracy for each iteration.
DESCRIPTION: A detailed study on various modes of CORDIC algorithm is done. First of all a study is made how the CORDIC algorithm is derived from the general vector equation. Then a study is done regarding the various modes of the CORDIC algorithm and how it can be used to find the sine, cosine, tan and logarithm functions, its use in conversion of coordinate systems. An attempt is made to carry out a rigorous study of its use in DSP oriented applications AND how it has revolutionized the DSP scenario. Finally simulations are carried out using MATLAB to support the purpose of our study.
RESULTS The results clearly bring out the advantage of using CORDIC algorithm. First of all the sine and cosine of any angle could be found out easily. Similar is the case of logarithm and hyperbolic functions. The simulation results prove the fact that the hardware complexity gets reduced by using the CORDIC algorithm. A large no of plots were obtained for different 7 functions. Finally the implementation in DCT was carried out and the results obtained were in line with those of the theoretical values.
CONCLUSION The CORDIC algorithms presented in this paper are well known in the research and super computing circles. Here the basic CORDIC algorithm and a partial list of potential applications of potential applications of a CORDIC based processor array to digital signal processing is presented. The CORDIC based DCT architecture for low power design has been proposed. The proposed multiplierless CORDIC based DCT architecture produces high throughput and is easy to implementing VLSI. The proposed architecture reduced the input data range for the CORDIC processor by split and the no of compensation iterations in CORDIC based DCT computation by utilizing that most images have similar neighboring pixels. The project also shows that a tool is available for use in FPGA based computing machines, which are the likely basis for the next generation DSP systems.