In this work, we consider a discrete-time switched linear system. A novel approach is introduced to estimate its state in a finite fixed time which can be arbitrarily chosen and is independent of the initial state. For cases where the additive disturbance and measurement noise are known, we provide an exact estimation. Otherwise, a finite-time interval observer is designed. The crucial idea is based on using past values of the input and output of the studied system and a minimal dwell time condition. Simulation results are provided to illustrate the effectiveness of the proposed techniques in different scenarios of finite time choices.