Fixed point implementation of trigonometric function using Taylor's series and error characterization

The aim of this paper is to analyze fixed point implementation of functions designed for signal processing algorithms. In this paper, basic building block function is analyzed for errors while implementing the algorithm using fixed point technique. To streamline the process of converting the floating point to fixed point, Model Based Design(MBD) concept is adopted where models of the basic functions are designed and tested in MATLAB (Matrix Laboratory) environment before converting to fixed point. Hardware Description Language (HDL) coder is used to convert the model in VHSIC Hardware Description Language (VHDL) code to implement in Field Programmable Gate Array (FPGA). The work proposed in this paper is abstract function which is implemented using Taylor's approximation series as some functions are not supported by HDL code generation tool for inverse trigonometric functions like inverse sine (ARCSINE), inverse tangent (ARCTANGENT). These functions are calculated with different number of iterations in MATLAB and using HDL coder. The script is successfully converted to fixed point VHDL code and the error between floating and fixed point is calculated which is presented in this paper