Fault diagnosis of rotating machinery is very important to guarantee the safety of manufacturing. Periodic impulsive fault features commonly appear in vibration measurements when local defects occur in the key components like rolling bearings and gearboxes. To extract the periodic impulses embedded in strong background noise, wavelet transform (WT) is suitable and has been widely used in analyzing these nonstationary signals. However, a few limitations like shift-variance and fixed frequency partition manner of the dyadic WT would weaken its effectiveness in engineering application. Compared with dyadic WT, the dual-tree rational dilation complex wavelet transform (DT-RADWT) enjoys attractive properties of better shift-invariance, flexible time-frequency (TF) partition manner, and tunable oscillatory nature of the bases. In this article, an impulsive fault features extraction technique based on the DT-RADWT is proposed. In the routine of the proposed method, the optimal DT-RADWT basis is constructed dynamically and adaptively based on the input signal. Additionally, the sensitive wavelet subband is chosen using kurtosis maximization principle to reveal the potential weak fault features. The proposed method is applied on engineering applications for defects detection of the rolling bearing and gearbox. The results show that the proposed method performs better in extracting the fault features than dyadic WT and empirical mode decomposition (EMD), especially when the incipient fault features are embedded in the frequency transition bands of the dyadic WT.