SEW: A full-spectrum linear fitting with stellar population synthesis method Based on "Equivalent Widths spectrum"

Abstract: We present a full-spectrum linear fitting method, SEW, for stellar population synthesis based on equivalent widths (EWs) to extract galaxy properties from observed spectra. This approach eliminates the need for prior assumptions about dust attenuation curves, which are instead derived as outputs of the fitting process. By leveraging the invariance of EWs and employing the Discrete Penalised Least Squares (DPLS) method to extract EWs, we address the nonlinear aspects of the fitting process by linearising the matrix equations. This enables accurate recovery of key parameters, stellar age, metallicity and dust attenuation, even under systematic calibration biases and varying attenuation conditions. Rigorous testing with mock spectra across signal-to-noise ratios (S/N = 5-30) and calibration biases demonstrates the robustness of method. The derived attenuation curves align closely with input models, and stellar population parameters are recovered with minimal bias. To facilitate adoption, we implement this method as a Python extension package for \texttt{pPXF} (\texttt{pPXF-SEW}). Our work addresses critical degeneracies in traditional spectral fitting and enhances the reliability of extragalactic studies.