Inverse Z-transform of a rational function

### 13.6.2 Inverse Z-transform of a rational function

The inverse Z-transform of a rational expression is a formula for the general term of a sequence with the given rational expression as its Z-transform. The invztrans command finds the inverse Z-transform of a rational expression.

- invztrans command takes one mandatory and two optional arguments:
  - rat, a rational expression.
  - Optionally, x the variable (by default x).
  - Optionally, n, a variable to be used by the result (by default x).
- ztrans(rat ⟨,x,n ⟩) returns the inverse Z-transform of rat.

#### Examples

invztrans(x/(x-1))

1 |  |  |  |  |  |  |  |  |  |

since ztrans(1) yields x/x−1.

invztrans(z/(z-1),z,n)

1 |  |  |  |  |  |  |  |  |  |

invztrans(x/(x-1)^2)

x |  |  |  |  |  |  |  |  |  |

invztrans(z/(z-1)^2,z,n)

n |  |  |  |  |  |  |  |  |  |