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A method of fault signature generation is presented that is based upon state space analysis of linear circults. An input control sequence is designed to reduce a nontrivial initial state of the circuit under test to the zero state in finite time. The realization of this stimulus as a piecewise constant waveform has step amplitudes that are exponential functions of the poles of the circuit under test. Perturbations of these amplitudes, engendered by element drift failure, constitute a fault signature. Single element value perturbations engender fault signature trajectories in signal space, and the fault dictionary is constructed by defining disjoint decision regions (hypervolumes) around each fault signature trajectory in the signal space. Circuit zeros of transmission allow the dimension of the signal space to be augmented with perturbation of such response waveform parameters as zero crossings. The theory of stimulus design for fault isolation in linear networks and a generalized matrix inverse method for computing the stimulus amplitudes from the pulse response of strictly proper circuits are presented. Examples of response waveforms and fault signature trajectories are given for several circuits.