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, which may lead to misattributing HRD-induced effects to noise reduction methods during evaluation. Insufficient understanding of the correspondence between system physical parameters and the distribution of envelope amplitude spectra often results in empirical selections of sensor placement, filtering frequency bands, and bearing rotational speed in engineering tests. Improper selections may cause missed diagnoses. To address these issues, this study constructs an equivalent 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.