How do I find the difference equation from a transfer function?

1. How do you find the difference equation from Z-transform?
2. Is a transfer function a differential equation?

How do you find the difference equation from Z-transform?

In order to solve the difference equation, first it is converted into the algebraic equation by taking its Z-transform. Then, the solution of the equation is calculated in z-domain and finally, the time-domain solution of the equation is obtained by taking its inverse Z-transform.

Is a transfer function a differential equation?

The transfer function can be obtained by inspection or by by simple algebraic manipulations of the differential equations that describe the systems. Transfer functions can describe systems of very high order, even infinite dimensional systems gov- erned by partial differential equations.