Disturbance observers have been used to estimate the disturbance in the plant. Several paperson design methods of disturbance observers have been published. Recently, the parameterizationof all disturbance observers for discrete-time plants with any output disturbance was clarified. However,no paper examines the parameterization of all disturbance observers for discrete-time plants withany input disturbance. In this paper, we clarify existance conditions of a disturbance observer and ofa linear functional disturbance observer for discrete-time plants with any input disturbance. Underthese conditions, we propose parameterizations of all disturbance observers and all linear functionaldisturbance observers for discrete-time plants with any input disturbance.