Field-Programmable Gate Array-Based Ultra-Low Power Discrete Fourier Transforms for Closed-Loop Neural Sensing

Digital implementations of discrete Fourier transforms (DFT) are a mainstay in feature assessment of recorded biopotentials, particularly in the quantification of biomarkers of neurological disease state for adaptive deep brain stimulation. Fast Fourier transform (FFT) algorithms and architectures present a substantial power demand from onboard batteries in implantable medical devices, necessitating the development of ultra-low power Fourier transform methods in resource-constrained environments. Numerous FFT architectures aim to optimize power and resource demand through computational efficiency; however, prioritizing the reduction of logic complexity at the cost of additional computations can be equally or more effective. This paper introduces a minimal-architecture single-delay feedback discrete Fourier transform (mSDF-DFT) for use in ultra-low-power field programmable gate array applications and shows energy and power improvements over state-of-the-art low-power DFT and FFT methods. In a neural sensing application, we observe a 33% reduction in dynamic power and 4% reduction in resource utilization when compared to state-of-the-art FFT algorithms; 38% reduction in dynamic power and 4% reduction in resource utilization when compared to Goertzel Algorithm. While designed for use in closed-loop deep brain stimulation and medical device implementations, the mSDF-DFT is also easily extendable to any ultra-low-power embedded application.