Accurate diagnosis of faults in transformers can significantly enhance the safety, reliability, and economics of power systems. In the case of a fault, it has been established that the pattern of the fault currents contain a typical signature of the nature and location of the fault for a given winding. This paper describes a new approach using wavelet transform (WT) for extraction of features from the impulse test response of a transformer in time-frequency domain and support vector machine in regression mode to classify the patterns inherent in the features extracted through the WT of different fault currents. This paper also describes an approach to identify the type and location of the transformer faults accurately by analyzing experimental impulse responses that contain noise. Here, experimental impulse responses have been preprocessed with the help of wavelet-packet filters to remove the unwanted noise from the signal and thereby enhance the analyzing capability of continuous wavelet transform.