This thesis is concerned with fast, reliable classification and identification of radio transmitters based on an analysis of their turn-on transients. Since the transients are unique, they are called the fingerprints of the corresponding radio transmitters. Major tasks in a radio transmitter identification system are: separating a transient from the channel noise; extracting important features contained in the transient; and classifying the transient based on these features. A system developed in this thesis achieves noise segmentation using the variance fractal dimension trajectory, with a modified triggering technique which improves the segmentation consistency. A variance fractal amplification technique is used for feature enhancement. Multifractal modelling of transients based on their strange attractors is also used in this thesis to investigate the suitability of such compact representations in transient classification. Preprocessing of the probabilistic neural network (PNN) using the principal component analysis (PCA) and the self-organizing feature map (SOFM) is performed to reduce the dimensionality of the PNN inputs and to cluster inputs, thus improving the training and classification speed. Experimental results show that the radio transmitter identification system is faster than the previous implementations. More specifically, the training time for a network consisting of 400 transients can be reduced to about a half of the original training time, 241 seconds. The system can classify radio transmitters not only according to their manufacturers and models, but also serial numbers, with he average classification rate around 97%.