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This paper presents the time domain and time-frequency domain analysis results of incipient events in single-phase distribution transformers. This analysis aids in the development of an automatic detection method for internal incipient faults in the transformers. The detection method can provide information to predict failures ahead of time so that the necessary corrective actions are taken to prevent outages and reduce down times. The analyzed data was obtained from simulations and experiments. Time-frequency analysis was performed using discrete wavelet transform (DWT). The obtained results are discussed.