Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity

03/27/2022

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by   Kaan Gokcesu, et al.

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We propose a multi-tone decomposition algorithm that can find the frequencies, amplitudes and phases of the fundamental sinusoids in a noisy observation sequence. Under independent identically distributed Gaussian noise, our method utilizes a maximum likelihood approach to estimate the relevant tone parameters from the contaminated observations. When estimating M number of sinusoidal sources, our algorithm successively estimates their frequencies and jointly optimizes their amplitudes and phases. Our method can also be implemented as a blind source separator in the absence of the information about M. The computational complexity of our algorithm is near-linear, i.e., Õ(N).