Abstract: The Hilbert resonance demodulation (HRD) technique is widely applied in bearing fault diagnosis. Current studies typically evaluate noise reduction methods based on the frequency components of envelope signals. However, there is a lack of quantitative analysis regarding the generation process of these frequency components. This might lead to misattributing HRD-induced effects to noise reduction methods during evaluation. In engineering, the empirical selection of test conditions and analysis parameters often results in missed diagnoses due to improper choices. To address these issues, this study constructs a fault signal model for vibration responses of rolling bearing outer race local faults. Through quantitative analysis of the Hilbert resonance demodulation process, the mapping relationship between signal parameters and envelope amplitude spectra is revealed. By investigating the influence of system physical parameters—such as natural frequency, damping ratio, and rotational speed—on signal characteristics, the correspondence between these parameters and the envelope amplitude spectrum distribution is established. This provides a clearer theoretical foundation for HRD applications. Simulated vibration signals processed by HRD demonstrate consistency with theoretical derivations, and experimental validation confirms the analytical conclusions based on the HRD demodulation mechanism.