[Paper Review] SpectRes: A Fast Spectral Resampling Tool in Python

Adam C. Carnall|arXiv (Cornell University)|May 15, 2017

Spectroscopy and Chemometric AnalysesChemistry86 citations

TL;DR

SpectRes is a Python function that resamples spectral flux densities (and uncertainties) onto arbitrary wavelength grids, preserving integrated flux with fast performance and covariance handling.

ABSTRACT

I present a fast Python tool, SpectRes, for carrying out the resampling of spectral flux densities and their associated uncertainties onto different wavelength grids. The function works with any grid of wavelength values, including non-uniform sampling, and preserves the integrated flux. This may be of use for binning data to increase the signal to noise ratio, obtaining synthetic photometry, or resampling model spectra to match the sampling of observed data for spectral energy distribution fitting. The function can be downloaded from https://www.github.com/ACCarnall/SpectRes.

Motivation & Objective

• Motivate the need for fast, accurate spectral resampling onto arbitrary wavelength grids.
• Provide a method to preserve total flux during resampling of spectra with associated uncertainties.
• Enable rapid applications such as binning to improve SNR, synthetic photometry, and matching model spectra to observed data for SED fitting.

Proposed method

• Compute a matrix P_ij representing the fraction of each original bin i that falls under each new bin j.
• Estimate new flux f_lambda_j as a weighted sum f_lambda_j = sum_i c_ij f_lambda_i, where c_ij = P_ij w_i / sum_i P_ij w_i.
• Propagate uncertainties to obtain sigma_j^2 = sum_i c_ij^2 sigma_i^2 (assuming independence).
• Construct covariance matrix between new bins using Y_j = sum_i c_ij X_i and Cov(Y_j, Y_b) = sum_i c_ij c_ib sigma_i^2, highlighting bin covariances.
• Note: SpectRes provides an optimized implementation for speed and can also return resampledErrs when provided.
• The code and numerical examples demonstrate substantial speed gains on large model spectra (e.g., Bruzual & Charlot 2003 model suite) and practical applications like rapid photometric redshift calculation.

Experimental results

Research questions

• RQ1 How can spectral data be resampled onto an arbitrary wavelength grid while conserving total flux?
• RQ2 How should uncertainties be propagated and covariances between resampled bins be treated during spectral resampling?
• RQ3 How does SpectRes perform in terms of speed on large spectral datasets, and what are practical use cases (e.g., photometric redshifts, SED fitting)?

Key findings

• Resampling a large Bruzual & Charlot model grid (221 models × 6917 points) to a uniform 5 Å grid takes ~40 ms.
• Resampling a single model to a uniform 20 Å grid for photometric fitting takes ~10 ms.
• The method preserves integrated flux and provides uncertainty propagation for each resampled bin.
• A covariance matrix is derived to quantify correlations between resampled fluxes due to shared original data.
• SpectRes is available on GitHub for download and use.