 
 
 
The Z-transform of a sequence a0, a1, …, an, … is the function
| f(z) = | 
 | 
 | . | 
The ztrans command takes one or three arguments.
ztrans returns the Z-transform of the sequence.
For example, the Z-transform of the sequence
| 0, 1, 2, 3, … | 
is
| f(z) = 0 + 1/z + 2/z2 + 3/z3 + … | 
which has closed form
| f(z) = z/(z−1)2. | 
Input:
Output:
Input:
Output:
Note that
Input:
Output:
since
| 
 | 1/xn = 1/(1−1/x) = x/(x−1). | 
We also have
Input:
Output:
Note that differentiating both sides of
| 
 | 1/zn = z/(z−1) | 
gives us
| 
 | n/zn−1 = 1/(z−1)2 | 
and so, multiplying both sides by z,
| 
 | n/zn = z/(z−1)2 = z/(z2 − 2z + 1) | 
as indicated above.
 
 
