The generation of internal gravity waves in the ocean with an arbitrary distribution of the buoyancy frequency generated by a moving source of perturbations is considered. The basic dispersion characteristics determining the properties of the generated far wave fields are studied analytically and numerically. The results of numerical computations of internal wave fields for different generation modes are presented. It is shown that the far wave fields of a separate mode can be presented as a sum of wave trains. The article investigates the specific characteristics of how these wave trains are generated. The proposed approach can be used to model internal wave wakes from a moving typhoon.