Accurate AM-FM signal demodulation and separation using nonparametric regularization method

Abstract In this paper we propose a novel adaptive nonparametric regularization (NPR) method for solving optimization problems with linear constraint. The regular parameter in NPR algorithm is adaptively updated. We prove that the NPR is convergent and provide an early stop method (ESM) with a termination criterion to handle the perturbation problem which is unsolved in other methods such as the augmented Lagrange method (ALM). We then introduce a new differential operator which can absolutely annihilate the amplitude-modulated and frequency-modulated (AM-FM) signals (AM-FM operator, AFO). The proposed operator is a precise operator and thus can obtain a more accurate solution in operator based signal demodulation and separation problems. We apply the NPR algorithm in signal demodulation and separation based on the AFO and propose signal demodulation (NPR-AFOSD) and separation (NPR-AFOSS) algorithms. The experimental results on both synthetic AM-FM signals and the real-life data demonstrate that the proposed demodulation and separation methods are more effective and robust than the state-of-the-art methods.