Rubber band filters: optimal padding without edge artifacts

TL;DR

This paper introduces the rubber band filter, an innovative padding method for bandpass filtering that eliminates edge artifacts in spectroscopy, demonstrating superior performance across multiple spectroscopic techniques.

Contribution

The paper presents a novel rubber band filter technique that provides optimal padding to prevent boundary artifacts during band-limited filtering in spectroscopy.

Findings

Eliminates boundary artifacts in spectral filtering.

Requires only a few additional Fourier transforms.

Proven effective across various spectroscopic methods.

Abstract

Bandpass filtering techniques are widely used in spectroscopy. However, conventional symmetric-padding filtering methods introduce boundary artifacts that distort the signal at the edges. We present a rubber band filter: a robust method for achieving band-limited filtering without these detrimental edge artifacts. The technique applies an optimal padding scheme during the filtering process, thereby overcoming longstanding challenges in achieving artifact-free filtering. Importantly, it is iterative and requires only a few extra Fourier transforms over conventional approaches. We demonstrate its superiority and versatility by applying it to three spectroscopic examples -- time-domain spectroscopy, Fourier-transform spectroscopy, and dual-comb spectroscopy.