With the development of distribution networks, distribution cables have been widely utilized, making maintenance of these cables crucial. Currently, there is limited research in China on the localization of local defects in cables based on wide-band impedance spectroscopy. To meet the precision requirements of intelligent inspection in distribution networks, this paper conducts research on the localization of local defects in distribution cables based on wide-band impedance spectroscopy. This paper investigates the localization of defects in power cables based on wideband impedance spectroscopy. Firstly, a mathematical and physical model of impedance spectroscopy under distributed parameter cables is derived based on transmission line theory. Subsequently, a wide-band impedance spectroscopy model incorporating local defects is developed using this model. Then, a method for localizing cable defects using a generalized orthogonal function-based integral transform is proposed. The correctness of the algorithm is validated through simulations conducted in the Matlab environment. The research presented in this paper provides a novel approach to defect localization in power cables, offering practical value and potential for further applications.