Abstract: Traveling-wave-based fault detection is on the basis of traveling wave transmission characteristic, refraction and reflection mechanism. The fault characteristics of wideband traveling wave under the time-frequency domains were deeply analyzed in this paper. Full-waveform representation of the traveling wave by fusing the characteristics in time-frequency domains was proposed. The relationship between the full-waveform and the topology structure, fault location, transmission characteristics, refraction and reflection process was deeply excavated. And then the correlation and difference of the full-waveform was qualitatively analyzed under different fault locations. On the basis, the full-waveform identification method based on waveform matching technology was presented, which can quantitatively conclude the correlation and difference. The proposed principle was comprehensively used the fault information in the time-frequency domains, which had a clearly physical significance. It forms a new theoretical foundation for the traveling-wave-based fault detection.