Real-Time Implementation and Characterization of the Sparse Fourier Transform for Spectral Measurements

This work presents the implementation and metrological validation of a Million-Point Sparse Fourier Transform (MP-SFT) on a Xilinx RFSoC platform for high-resolution spectral analysis. As FFT-based methods become inefficient for a large number of points or sparse signals, the proposed system exploits inverse modulo permutations, windowed subsampling, and randomized hashing to reconstruct only the significant spectral components. A hybrid hardware-software architecture is adopted: the Programmable Logic (PL) performs real-time data acquisition and parallel subsampled FFT processing, while a host workstation executes the final reconstruction through de-hashing, voting, and amplitude estimation. A calibration procedure based on polynomial regression ensures accurate reconstruction across the [10], [951] MHz range. Performance was evaluated in terms of Spurious-Free Dynamic Range (SFDR) and accuracy. Experimental results show an SFDR up to 65.2 dB, limited mainly by a clock-related spur at 491.52MHz. The system exhibits reconstruction accuracy better than 0.08 dB for input amplitudes between -10 dBm and -40 dBm, confirming linearity and robustness. These results demonstrate the feasibility of hardware-accelerated sparse spectral estimation on heterogeneous platforms and provide a foundation for future extensions toward full hardware reconstruction and real-time analysis of adaptive or non-stationary signals.