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An analog-digital system for implementation of the robust time-frequency distributions is proposed. It provides an efficient real-time analysis of nonstationary signals corrupted by heavy-tailed noise. The most important part of this system is the realization of the L-estimate short-time Fourier transform that requires sorting operation. The proposed solution is designed to execute sorting operation within a single clock cycle, regardless of the number of inputs. The performance of the proposed hardware is tested on a real signal example.