The inverse Z-transform of a rational function: invztrans

### 5.63.2 The inverse Z-transform of a rational function: invztrans

The invztrans command takes one or three arguments.

- A rational expression in the variable x, or
- A rational expression, the variable used in the expression, and a variable to be used by the result.

ztrans returns the inverse Z-transform, namely a formula for the general term of a sequence with the given rational expression as its Z-transform.

Since ztrans(1) = x/(x-1), we get
Input:

invztrans(x/(x-1))

Output:

1

Input:

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

Output:

1

Similarly,
Input:

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

Output:

x

Input:

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

Output:

n