Adaptive Integral Operators for Signal Separation

The operator-based signal separation approach uses an adaptive operator to separate a signal into a set of additive subcomponents. In this paper, we show that differential operators and their initial and boundary values can be exploited to derive corresponding integral operators. Although the differential operators and the integral operators have the same null space, the latter are more robust to noisy signals. Moreover, after expanding the kernels of Frequency Modulated (FM) signals via eigen-decomposition, the operator-based approach with the integral operator can be regarded as the matched filter approach that uses eigen-functions as the matched filters. We then incorporate the integral operator into the Null Space Pursuit (NSP) algorithm to estimate the kernel and extract the subcomponent of a signal. To demonstrate the robustness and efficacy of the proposed algorithm, we compare it with several state-of-the-art approaches in separating multiple-component synthesized signals and real-life signals.