mSDF-DFT: An ultra-low energy discrete Fourier transform architecture for closed-loop neural sensing

Digital implementations of the discrete Fourier transform (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 energy demand from onboard batteries in implantable medical devices, necessitating the development of ultra-low energy Fourier transform methods in resource-constrained environments. Numerous FFT architectures aim to optimize energy and resource consumption through computational efficiency; however, prioritizing logic complexity reduction at the expense 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-energy field-programmable gate array applications and demonstrates energy and power improvements over benchmark low-energy DFT and FFT methods. Across the parameter set, we observed 11.1% median resource usage reduction and 5.0% median energy reduction when compared to a gold standard SDF-FFT algorithm; 38.1% median resource reduction and 8.8% median energy reduction when compared to the 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-energy embedded application.