The increasing integration of distributed energy resources (DERs) into the distribution system has caused interference with the signals stimulated by high impedance faults (HIFs). Many existing HIF detection or location methods that are only based on the superficial nonlinearity features of signals rather than the deep laws, will become invalid. This paper proposes a detection and location scheme for HIFs by theoretically analyzing the relationships between signals and systems. By establishing the equivalent circuit of a resonant distribution system, an online method to calculate the kernel system parameters is proposed, based on which an adaptive criterion for HIF detection is provided. In this way, the ability to detect HIF is adequately exploited and independent of DER influences. The method is able to detect HIF over 8.5 $\text{k}{\Omega }$ under common operating conditions. Furthermore, the nonlinearity of HIF is analyzed by deriving laws about how wideband signals distribute in the system. The $3^{\mathrm{ rd}}$ harmonic component of zero-sequence signals is proved to be superior in HIF location in terms of signal content and discrimination, which is also demonstrated to be valid under the influence of DER harmonic injection. On this basis, a HIF location method utilizing the $3^{\mathrm{ rd}}$ harmonic zero-sequence signals is proposed. The effectiveness of the method and its robustness to the DER interference are validated by simulated and field HIFs in 10kV systems.