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

arXiv: https://arxiv.org/abs/2203.14324 · HTML: https://mlsanity.com/paper/2203.14324/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 77 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions](https://mlsanity.com/paper/2201.07164/) (2022)
- [Cumulative Regret Analysis of the Piyavskii--Shubert Algorithm and Its Variants for Global Optimization](https://mlsanity.com/paper/2108.10859/) (2021)
- [Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics](https://mlsanity.com/paper/2202.11141/) (2022)
- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)

## Built on by (most cited first, 1 of 1)

- [Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interference](https://mlsanity.com/paper/2204.08411/) (2022)

## Abstract (arXiv)

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., tildeO(N).