This study presents a methodology for analysing the transient behaviour of harmonics associated with the interfacing of a synchronous generator and a transmission line. The algorithm is derived entirely in the dynamic harmonic domain that is based on an orthogonal basis and on operational matrices. The main characteristics of the proposed method are: its capability to accurately follow the harmonic content of a transient without the aid of a post-processing tool and its ability to serve as a visually active indicator of the steady-state and transient conditions in a signal. The proposed method is validated by comparing its results against those obtained through a time-domain technique.