<p>A centrifugal pump is a complex system composed of multiple interacting components. Under real industrial conditions, compound faults—particularly those involving both impulsive and non-impulsive characteristics—are difficult to detect and distinguish. In this study, a novel filterbank, termed the adaptive analytical wavelet packet transform (AAWPT), is proposed for the identification of compound faults in rotary machinery. This filterbank is designed to extract a specific mode corresponding to each type of fault, whether impulsive or non-impulsive. As a result, this research pioneers a dedicated mode for non-impulsive faults, leading to a significant enhancement in the diagnosis of these faults within machines exhibiting compound fault conditions. To validate the effectiveness of the proposed method, it was applied to fault diagnosis in a centrifugal pump operating in a noisy industrial environment. Compared to previous studies, the results demonstrate that the AAWPT successfully identifies distinct modes for impulsive faults (e.g., bearing defects and misalignment) and non-impulsive faults (e.g., cavitation) across various rotational speeds.</p>