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The Spectral Properties of the Magnetic Polarizability Tensor for Metallic Object Characterisation

The measurement of time-harmonic perturbed field data, at a range of frequencies, is beneficial for practical metal detection where the goal is to locate and identify hidden targets. In particular, these benefits are realised when frequency dependent magnetic polarizability tensors (MPTs) are used to provide an economical characterisation of conducting permeable objects and a dictionary based classifier is employed. However, despite the advantages shown in dictionary based classifiers, the behaviour of the MPT coefficients with frequency is not properly understood. In this paper, we rigorously analyse, for the first time, the spectral properties of the coefficients of the MPT. This analysis has the potential to improve existing algorithms and design new approaches for object location and identification in metal detection. Our analysis also enables the response transient response from a conducting permeable object to be predicted for more general forms of excitation.