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• Intrinsic Time-scale Decomposition and Graph Signal Processing is integrated. • A PR component with minimum Laplacian Energy index is chosen. • The ITD-GSP can precisely provide the characteristic frequency of compound faults. • The ITD-GSP algorithm is insensitive to the installation direction of sensors. The diagnosis of compound faults of rolling bearing is extremely difficult due to the nonlinearity and non-stationary of signal. With the purpose of extracting the compound faults from rolling bearings of aero-engine, efforts were made to integrate Intrinsic Time-scale Decomposition (ITD) and Graph Signal Processing (GSP), namely the ITD-GSP methodology. A PR component (obtained by ITD algorithm) with minimum Laplacian Energy (LE) index is chosen as the optimal rotational component to identify types of compound fault of rolling bearing. The result indicates that the proposed ITD-GSP methodology can precisely and effectively provide the characteristic frequency of compound faults no matter in which direction of sensors (vertical and horizontal) and which type of compound faults of rolling bearing. On the contrary, the mainstream schemes of fault analysis using ITD algorithm (correlation coefficients or kurtosis as the basis to screen optimal rotational component) cannot. [ABSTRACT FROM AUTHOR]