Separation of noisy multitone signals based on variational mode decomposition

Abstract

We have observed that Variational Mode Decomposition (VMD) exhibits instability in the denoising and separation of noisy multitone signals. Specifically, minor changes in factors such as signal-to-noise ratio, frequency spacing, sampling rate, and probability distribution can significantly impact the decomposition results. To address this issue, we have developed the Dual-VMD-correlation algorithm. This algorithm effectively mitigates the impact of beat effects when harmonics of closely spaced frequencies are superimposed, enabling stable denoising of noisy multitone signals and the separation of each individual tone signal. The algorithm holds promise for applications in frequency-modulated continuous wave laser detection. It can address challenges related to denoising laser echo signals interfered with by aerosols and the difficulty in separating backscatter interference from the target reflected signal spectrum.