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

## TL;DR

This paper provides a rigorous spectral analysis of magnetic polarizability tensor coefficients across frequencies, enhancing understanding for improved metal detection and object identification algorithms.

## Contribution

It offers the first detailed spectral analysis of MPT coefficients, aiding in better algorithm design for metal detection and object characterization.

## Key findings

- Spectral properties of MPT coefficients are characterized across frequencies.
- Analysis enables prediction of transient responses for various excitations.
- Potential to improve existing metal detection algorithms.

## Abstract

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.