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This paper proposes a method to quickly and efficiently compute the voltageand current along a transmission line which can be "damaged"; that is itselectrical properties can be unevenly distributed. The method approximates atransmission line by a self-similar circuit network and leverages our previouswork regarding the frequency response for that class of networks. The mainmotivation arises from the research for railway track circuit systems wheretransmission line models are often employed. However, in contrast to realtransmission lines, railway track circuits are more likely to be damaged due toits scale and environmental uncertainties; furthermore, changes in circuitproperties due to a train occupying a segment of the track also is of greatinterest as a means to ensure safety. As a result, an accurate and quicksimulation of damaged track circuits is necessary and can contribute to thecorresponding health monitoring research area in the future.

Frequency Response of Transmission Lines with Unevenly Distributed Properties with Application to Railway Safety Monitoring