Some weak frequency components are important to fault diagnosis, but they sometimes cannot be discovered by using general signal processing methods. To extract from the important components from vibration signal efficiently, an equivalent power spectrum analysis approach is proposed in this paper which applies the Redundant Wavelet Transform (RWT) decomposition by using an orthogonal wavelet as a basis function. The new approach makes full use of multi-resolution information which obtained by the RWT decomposition. As a result, submerged frequency components are revealed. The proposed approach has been used for friction fault diagnosis of a gas turbine effectively.