Matlab State-Space Filter Conversion Example

Here is the example of §5.13.5 repeated using matlab.^E.9 The difference equation

$$y(n) = u(n-1) + u(n-2) + 0.5\, y(n-1) - 0.1\, y(n-2) + 0.01\, y(n-3)$$

corresponds to the transfer function

$$H(z) = \frac{B(z)}{A(z)} = \frac{z^{-1}+ z^{-2}}{1 - 0.5\,z^{-1}+ 0.1\,z^{-2}- 0.01\,z^{-3}},$$

so that in matlab the filter is represented by the vectors

NUM = [0  1   1    0   ]; % NUM and DEN should be same length
DEN = [1 -0.5 0.1 -0.01];

The tf2ss function converts from ``transfer-function'' form to state-space form:

 [A,B,C,D] = tf2ss(NUM,DEN)
A =
   0.00000   1.00000   0.00000
   0.00000   0.00000   1.00000
   0.01000  -0.10000   0.50000

B =
  0
  0
  1

C =
  0  1  1 

D = 0