Fast Fourier Transform Implementation Project as an FPGA Learning Tool

This paper presents the design and implementation of a 16-point Fast Fourier Transform (FFT) using fixed-point arithmetic in SystemVerilog, focusing on its value as a learning tool in FPGA-based education. Bridging theoretical principles and practical application, the project begins with a Python prototype, transitioning to a hardware-friendly design optimized for resource-constrained platforms like the Intel Cyclone IV E FPGA. Utilizing the radix-2 Cooley-Tukey algorithm, the design emphasizes modularity, computational efficiency, and clarity, addressing challenges such as limited I/O pins, precision constraints, and the absence of floating-point arithmetic through a Q1.15 fixed-point format. The implementation demonstrates the feasibility of real-time signal processing, achieving computation of the full transform within ten nanoseconds while maintaining accuracy within 1% of theoretical results. Beyond the technical achievements, the project provides an interactive educational framework for students, showcasing the trade-offs between performance, resource utilization, and hardware constraints in real-world engineering scenarios. Key educational benefits include hands-on experience with HDL programming, fixed-point arithmetic, and optimization for FPGA platforms. The project also explores methodologies for overcoming common pitfalls, such as managing resource imbalances and choosing between LUTs and formulas for computational efficiency. Suggestions for future enhancements, including cascading to larger FFT sizes, increasing precision with higher bit-widths, and exploring hybrid fixed-point and floating-point designs, highlight the potential scalability and versatility of this work. These advancements position the implementation as a scalable, practical, and pedagogical tool, enriching the learning experience and enabling students to tackle complex digital signal processing challenges.