A New Recursive Trigonometric Technique for FPGA-Design Implementation

Area of Science:

• Digital Signal Processing
• Computer Engineering
• Hardware Acceleration

Background:

• Traditional Field-Programmable Gate Array (FPGA) implementations of trigonometric functions rely heavily on lookup tables, consuming significant data storage.
• While Coordinate Rotation Digital Computer (CORDIC) algorithms reduce storage, they introduce complexity and lengthy implementation times.

Purpose of the Study:

• To introduce a novel recursive trigonometric (RT) technique for FPGA design.
• To enhance communication accuracy and decrease response times in FPGA implementations.
• To offer an alternative to traditional lookup table and CORDIC methods for trigonometric function generation.

Main Methods:

• The proposed RT technique utilizes trigonometric transformations for direct calculation of trigonometric functions.
• It avoids iterative computations, thereby minimizing computational errors.
• Accuracy is determined solely by the precision of the input values.

Main Results:

• The RT technique effectively generates highly accurate cosine waveforms.
• It bypasses the scale factor (K) related errors common in CORDIC implementations.
• Simulation tests on an FPGA verified the technique's performance.

Conclusions:

• The recursive trigonometric (RT) technique presents a viable and efficient method for implementing trigonometric functions on FPGAs.
• This approach offers improved accuracy and reduced computational complexity compared to existing methods.
• The RT technique is particularly effective for applications requiring precise cosine waveform generation in FPGAs.