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

TL;DR

This paper introduces a robust, nonparametric spectral peak decomposition method that efficiently handles distortion and interference, utilizing a pseudo-symmetric model and linear time complexity for spectral analysis.

Contribution

The proposed method offers a robust, efficient, and nonparametric approach to spectral peak decomposition that outperforms traditional waveform fitting techniques under distortion and interference.

Findings

Linear time complexity per spectral peak ($O(N)$)

Robustness against arbitrary distortion and noise

Spectral peaks exhibit pseudo-orthogonal behavior

Abstract

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.