Calculations are made of the propagation of internal gravity waves (IGW) from unsteady sources located in the troposphere. Taking the unsteadiness of the tropospheric sources into account leads to a decrease in the heights of the maximum amplitudes and energy characteristics of these waves, owing to energy capture in the mesospheric waveguide at z approximately equals 75 km. The filtering action of the background wind leads mainly to intensification of the IGW, which propagate counter to the wind, and to the formation of wave accelerations which hamper the background flow near the mesopause. For certain source parameters and at certain moments of time IGW traveling in the same direction as the background wind may prevail.