Spectral decomposition results (middle) and fitting residuals (bottom) for DESI (left) and SDSS (right). The top panels are a zoom-in decomposition of the Hβ and Hα regions. Shown are: the observed spectral data (black line), the best-fit model (red), the power-law continuum (purple), the host galaxy template (violet), the Fe ii pseudo-continuum template (pink), the Balmer continuum (teal), the narrow components (grey), the blue wing components (BWC; blue), and the main core components (MCC; yellow). The grey-shaded region marks the fitting window (3040 Å to 7200 Å).