Energy-Efficient FPGA Solutions for Large-Scale FFTs and Non-Uniform FFTs A Software-Hardware Co-Design Approach for Radio Interferometry

The fast Fourier transform (FFT) is a cornerstone of digital signal processing, widely used in scientific and engineering applications, including radio interferometry imaging and medical imaging. However, traditional uniform FFT algorithms fall short in handling irregularly sampled data, leading to the development and essential role of non-uniform FFT (nuFFT) techniques. NuFFT is crucial for accurately processing and reconstructing data in applications such as radio interferometry, where the data collected from telescopes is often non-uniformly spaced, and in medical imaging modalities like MRI, which frequently utilize non-Cartesian sampling patterns. In this presentation, we propose a versatile software-hardware co-design methodology based on High Level Synthesis aimed at exploring and implementing energy-efficient FPGA solutions for large-scale FFT and nuFFT computations. We present insights derived from application-specific requirements for the radio interferometry domain, focusing on critical design parameters such as accuracy, nuFFT size, type, and the resolution of sky images. By systematically evaluating these parameters, we identify key tuning knobs for optimizing energy efficiency, performance, and accuracy. For instance, in radio interferometry, the desired sky image resolution and the distribution of sampling points dictate the precision and computational load of the nuFFT, which directly influence the hardware design. Similarly, in medical imaging, the type of nuFFT and required image fidelity are critical for fine-tuning the accelerator. We present a the initial results of our co-design process, demonstrating significant improvements in energy consumption and latency compared to traditional software implementations optimized for multicore CPU. Furthermore, we discuss the portability and scalability of the proposed solutions across different families of FPGAs from Intel and AMD. Both are crucial for extending the benefits of our solution to a wide range of applications, from large-scale radio interferometry arrays to portable medical imaging devices. This work paves the way for future research in developing more advanced, energy-efficient computational tools for high-impact scientific and medical applications.