The behavior of a linear sequential circuit can be described by the matrix equations where u, v, and σt are the input, output, and encoder state, respectively, at time t. a) Show that applying the...

The behavior of a linear sequential circuit can be described by the matrix equations

where u, v, and σt are the input, output, and encoder state, respectively, at time t.

a) Show that applying the D-transforms to each term in the matrices yields

where σ0 is the initial value of σt.

b) Show that the transfer function matrix is

c) Show that the abstract state s(D) corresponding to the encoder state σ can be expressed as