A novel high-speed fiber-optic spectrometer has been demonstrated in our previous work. The high-speed spectrum measurement is enabled by translating the spectral-domain signal into a time-domain signal through a dispersion element. We present a mathematical model that accurately describes the relationship between the optical spectrum to be measured and the dispersed time-domain signal. Based on the model, the effects of the key parameters on the performance of the spectrometer are investigated in detail using numerical simulation. The analysis is useful for the design and application of such spectrometers. (C) 2007 Optical Society of America.