In an audio-information encoding apparatus, in order to encode an audio signal containing a white-noise component, an index iL indicating the energy level of the white-noise component and an index iR designating the start index of a random-number table are introduced into a code train. The method uses a complement states grouping technique that comprises the steps of finding the state distances between complement states; forming the reduced-state trellis by grouping the complement states with state distance no less than the minimum free distance; and by keeping the complement states with state distance less than minimum free distance unchanged. This process can be carried on throughout a hierarchy of windows as the user browses for a destination window for the drag operation. The system also computes and displays object trajectories from the computed flight characteristics which account for the characteristics of the object and the atmospheric conditions.