In the note, a generalized disturbance observer capable of estimating higher order disturbances in the time series expansion is newly proposed. Initiated from a constant disturbance observer, we extend it systematically to cope with ramp disturbance and general order disturbances. The generalized form for disturbance observer exhibits the novel structure incorporating the system model and integrals. To be practical, the noisy measurement and the performance in the frequency domain are addressed. In addition, for a class of linear systems, an output-based disturbance observer of reduce order is newly derived from the proposed full state disturbance observer, and its potential applicability will be demonstrated by an example.