EECS20N: Signals and Systems

SISO Systems

For a single-input, single-output system, M = 1, K = 1, so Inputs = Outputs = Reals. (The state, however, is N-dimensional.) So

  • the N × 1 matrix B can be written as the column vector b = [b1, … , bN ]T ,
  • the 1 × N matrix C can be written as a 1 × N row vector cT = [c1 , … , cN ], and
  • the 1 × 1 matrix D can be written as a real number d.

With this notation s, b, c are all N × 1 column vectors.

The response of the system to an input sequence x(0), x(1), x(2), … is

s(n) = An s0 + ∑ (m = 0 to n-1) An-1-m b x(m)

y(n) = cT An s0 + ∑ (m = 0 to n-1) cT An-1-m b x(m) + dx(n).