The envelope following response (EFR) has been proposed as a non-invasive marker of synaptopathy in animal models. However, its amplitude is affected by the spread of basilar-membrane excitation and other coexisting sensorineural hearing deficits. This study aims to (i) improve frequency specificity of the EFR by introducing a derived-band EFR (DBEFR) technique and (ii) investigate the effect of lifetime noise exposure, age and outer-hair-cell (OHC) damage on DBEFR magnitudes. Additionally, we adopt a modelling approach to validate the frequency-specificity of the DBEFR and test how different aspects of sensorineural hearing loss affect peripheral generators. The combined analysis of simulations and experimental data proposes that the DBEFRs extracted from the [2-6]-kHz frequency band is a sensitive and frequency-specific measure of synaptopathy in humans. Individual variability in DBEFR magnitudes among listeners with normal audiograms was explained by their self-reported amount of experienced lifetime noise-exposure and corresponded to amplitude variability predicted by synaptopathy. Older listeners consistently had reduced DBEFR magnitudes in comparison to young normal-hearing listeners, in correspondence to how age-induced synaptopathy affects EFRs and compromises temporal envelope encoding. To a lesser degree, OHC damage was also seen to affect the DBEFR magnitude, hence the DBEFR metric should ideally be combined with a sensitive marker of OHC damage to offer a differential diagnosis of synaptopathy in listeners with impaired audiograms. Copyright © 2020 Elsevier B.V. All rights reserved.