  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.,
$\tilde{O}(N)$.
