We present the study of collinear light scattering by relatively short acoustic pulses in birefringent crystals providing that both the acoustic attenuation and spreading the acoustic beam are allowed for. The exact and closed analytical model for the phenomenon described is developed. The peculiarities of collinear acousto-optical interaction in the cells made of lithium niobate single crystal are considered for the traveling-wave regime. The feasibility of applying such an effect to perform a coherent optical processing of ultra-high frequency (UHF) radio-wave electronic pulses is analyzed and the corresponding opto-electronic algorithm is elaborated. The results of preliminary experiments, exhibiting an opportunity for the data processing in anti-radar system, are presented.