Vibrations of rotating machinery primarily originate from two sources, both of which are distorted by the machine's transfer function on their way to the sensor: the dominant gear-related vibrations and a low-energy signal linked to bearing faults. The proposed method facilitates the blind separation of vibration sources, eliminating the need for any information about the monitored equipment or external measurements. This method estimates both sources in two stages: initially, the gear signal is isolated using a dilated CNN, followed by the estimation of the bearing fault signal using the squared log envelope of the residual. The effect of the transfer function is removed from both sources using a novel whitening-based deconvolution method (WBD). Both simulation and experimental results demonstrate the method's ability to detect bearing failures early when no additional information is available. This study considers both local and distributed bearing faults, assuming that the vibrations are recorded under stable operating conditions.