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We propose a multi-tone decomposition algorithm that can find thefrequencies, amplitudes and phases of the fundamental sinusoids in a noisyobservation sequence. Under independent identically distributed Gaussian noise,our method utilizes a maximum likelihood approach to estimate the relevant toneparameters from the contaminated observations. When estimating $M$ number ofsinusoidal sources, our algorithm successively estimates their frequencies andjointly optimizes their amplitudes and phases. Our method can also beimplemented as a blind source separator in the absence of the information about$M$. The computational complexity of our algorithm is near-linear, i.e.,$\tilde{O}(N)$.

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