Intelligent fault diagnosis of rotating equipment is increasingly reliant on algorithms that are driven by big data. By contrast, signal processing was once widely utilized for fault diagnosis in machinery as a classical tool for signal analysis due to its capability to investigate the fault-related mechanism and almost no demand on the number of data samples. This investigation was motivated by the notion that signal processing and data-driven algorithms are combined to exploit their respective characteristics and strengths. Furthermore, in engineering practice, numerous complex factors such as time-variable operating conditions of equipment, non-stationary properties of signals, and extremely limited samples available for model training, can make it difficult to learn discriminative features from input data, thereby diminishing the diagnostic accuracy. In this paper, a novel framework of vibration amplitude normalization (VAN) enhanced fault diagnosis is proposed. Firstly, after dissects deeply the effects of the time-varying speed conditions on vibration signal and its characteristics, VAN technique is proposed for non-stationary signal processing to obtain the approximate stationary signal, so as to facilitate the subsequent state characteristics mining from the vibration signal. Then, two VAN enhanced fault diagnosis methods—ie signal amplitude normalization integrated with shallow learning by cascade and VAN integrated with deep learning by embedding—are developed to capture discriminative features from approximate stationary signal for fault diagnosis under conditions of variable speed and extremely limited samples. Finally, the feasibility and effectiveness of the proposed methods are verified using actual vibration datasets measured on test rig and in-site wind turbines. The number of samples required to achieve the same diagnostic accuracy is reduced by an average of 60%, demonstrating the superiority.