Rubber band filters: optimal padding without edge artifacts

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.