The behavior of the transmission response of an Acousto-Optic Tunable Filter (AOTF) in TeO2 is analyzed in response to acoustic pulse signal. With a quasi-collinear structure, the interaction length between acoustic and optical waves can be adjusted by controlling the duration of the acoustic pulses. We propose to study the selectivity and the side lobe levels of the optical transmission function for an RF signal modulated with rectangular and Hamming windows. The ability to adjust the transmission function over a large optical bandwidth can have very interesting applications. We use a model based on Fast Fourier Transform in order to predict the AOTF transmission function shape. We also have developed an experimental setup to measure the diffraction efficiency as a function of optical wavelengths using optical pulses. The use of acoustic pulses involves working with "long" optical pulses (a few µs) to freeze the acoustic wave in the cell during the acousto-optic interaction. We show that the apodization windows make it possible to significantly reduce the secondary lobes and to easily control the selectivity over a large optical wavelength band. Good agreements are observed between simulations and measurements.