A New Recursive Trigonometric Technique for FPGA-Design Implementation

Xing Xing; Wilson Wang

doi:10.3390/s23073683

A New Recursive Trigonometric Technique for FPGA-Design Implementation

Sensors (Basel). 2023 Apr 2;23(7):3683. doi: 10.3390/s23073683.

Authors

Xing Xing¹, Wilson Wang²

Affiliations

¹ Department of Electrical and Computer Engineering, Lakehead University, Thunder Bay, ON P7B5E1, Canada.
² Department of Mechanical Engineering, Lakehead University, Thunder Bay, ON P7B5E1, Canada.

Abstract

This paper presents a new recursive trigonometric (RT) technique for Field-Programmable Gate Array (FPGA) design implementation. The traditional implementation of trigonometric functions on FPGAs requires a significant amount of data storage space to store numerous reference values in the lookup tables. Although the coordinate rotation digital computer (CORDIC) can reduce the required FPGA storage space, their implementation process can be very complex and time-consuming. The proposed RT technique aims to provide a new approach for generating trigonometric functions to improve communication accuracy and reduce response time in the FPGA. This new RT technique is based on the trigonometric transformation; the output is calculated directly from the input values, so its accuracy depends only on the accuracy of the inputs. The RT technique can prevent complex iterative calculations and reduce the computational errors caused by the scale factor K in the CORDIC. Its effectiveness in generating highly accurate cosine waveform is verified by simulation tests undertaken on an FPGA.

Keywords: CORDIC; FPGA; LUT; digital signal processing; trigonometric functions.

Grants and funding

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Bare Point Water Treatment Plant in Thunder Bay, ON, Canada.