# Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interference

arXiv: https://arxiv.org/abs/2204.08411 · HTML: https://mlsanity.com/paper/2204.08411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 73 references that are in the map.
- First posted on arXiv 18 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [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)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [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)
- [Efficient, Anytime Algorithms for Calibration with Isotonic Regression under Strictly Convex Losses](https://mlsanity.com/paper/2111.00468/) (2021)
- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)
- [Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity](https://mlsanity.com/paper/2203.14324/) (2022)

## Abstract (arXiv)

We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum, we optimize the problem from a more robust perspective. We model the peaks in spectrum as pseudo-symmetric functions, where the only constraint is a nonincreasing behavior around a central frequency when the distance increases. Our approach is more robust against arbitrary distortion, interference and noise on the spectrum that may be caused by an observation system. The time complexity of our method is linear, i.e., O(N) per extracted spectral peak. Moreover, the decomposed spectral peaks show a pseudo-orthogonal behavior, where they conform to a power preserving equality.