Signals and Systems

ADDITIONAL SOLVED EXAMPLES

Example 10.9 Find the SV model for the system with

 

 

Solution

The given transfer function is

 

 

i.e.,        (z⁴ + 2z³ + 5z² + 6z + 3) Y(z) = U(z)

i.e.,        z⁴Y(z) + 2z³Y(z) + 5z²Y(z) + 6zY(z) = U(z)      (1)

The inverse transform of Eq. (1) gives

 

y(k + 4) + 2y(k + 3) + 5y(k + 2) + 6y(k + 1) + 3y (k) = u(k)

i.e.,        y(k + 4) = u(k) − 2y(k + 3) − 5y(k + 2) − 6y(k + 1) − 3y (k)

Using four delay elements y(k + 3), y(k + 2), y(k + 1) and y(k), we can get y(k + 4) which has been shown in Fig. E10.6.

 

 

Fig. ...