Time-fluctuating signals are ubiquitous and diverse in many physical, chemical, and biological systems, among which random telegraph signals (RTSs) refer to a series of instantaneous switching events between two discrete levels from single-particle movements. A reliable RTS analysis is a crucial prerequisite to identify underlying mechanisms related to device performance and sensitivity. When numerous levels are involved, complex patterns of multilevel RTSs occur and make their quantitative analysis exponentially difficult, hereby systematic approaches are often elusive. In this work, we present a three-step analysis protocol via progressive knowledge-transfer, where the outputs of the early step are passed onto a subsequent step. Especially, to quantify complex RTSs, we resort to three deep neural network architectures whose trained models can process raw temporal data directly. We furthermore demonstrate the model accuracy extensively with a large dataset of different RTS types in terms of additional background noise types and amplitude size. Our protocol offers structured schemes to extract the parameter values of complex RTSs as imperative information with which researchers can draw meaningful and relevant interpretations and inferences of given devices and systems.