A spectrum analyzer of optical signal based on an acousto- optic tunable filter (AOTF) is a sequential analyzing system where the scanning along the wavelengths is made by varying the control signal frequency. Traditionally, a chirp control signal is used in such systems, provided that the frequency variation rate in the cell's acoustical aperture is negligibly slow. In this case, the system spectral response replicates the amplitude frequency response of acousto-optic interaction. However, when the system speed are to be maximized, the frequency variation rate in the cell aperture has to be taken into account. Basing on the linear system theory, the paper presents the calculation of the spectrometer's output signal for a laser input optical beam, weak interaction approximation, and chirp RF control signal. The closed form equation is obtained using the stationary phase method. Basing on the obtained expression, the minimally possible time of analysis is obtained for the spectrometer based on the AOTF with the quasi-collinear interaction in the TeO2 crystal. The criterion was the 10 percent decrease in spectral resolution. The experimental results are in good agreement with the theoretical predictions.