An analytical description of distortion-free transmission using time-domain optical Fourier transformation (OFT) is newly developed by using a time-domain ABCD matrix formalism. The analysis is based on an analogy with a spatial Fourier transformation in diffraction through lenses. The theory enables us to derive the pulse width and chirp at the OFT output explicitly and to evaluate the effect of dispersion inaccuracy in OFT by using only simple algebra.