Chebyshev approximation technique: analysis and applications

Abstract

In many situations, exact solutions to complex problems may be challenging or impossible to obtain, making approximation techniques necessary for making informed decisions. Since function implementation on FPGAs can be difficult and resource-consuming, therefore it would be a better idea to approximate them. In this study, the Chebyshev approximation technique is thoroughly investigated, and an FPGA implementation is proposed and analyzed. This implementation will be compared to other implementations of approximation techniques with parameters such as accuracy, speed, and design size taken into consideration. Applications of this FPGA design are also discussed and shown such as approximating the sigmoid function for machine learning in an efficient manner. This study proved the adequacy of the Chebyshev approximation and its accelerated FPGA implementation for various applications including machine learning, filter design, signal processing, and many other practical applications in engineering and science.