This paper attempts to apply Walsh transforms to the state-space analysis of linear discrete-time systems. A cyclic shift-theorem of Wal’sh transforms presented by Cheng and Liu is first extended

and with the aid of Walsh transforms of the discrete state equations

a simple numerical formula for solving the state equations in the sequence domain is derived

from which a group of cyclic solutions of zero-state

response of a system can be obtained. An illustrative example is given.