Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity
This work addresses signal processing challenges in applications like audio or communications by providing an efficient method for separating sinusoidal sources, though it appears incremental as it builds on maximum likelihood approaches.
The paper tackles the problem of blind source separation for mixtures of sinusoids by proposing a multi-tone decomposition algorithm that estimates frequencies, amplitudes, and phases from noisy observations, achieving near-linear computational complexity of O(N).
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., $\tilde{O}(N)$.