• Laplace and Z Transforms
• Laplace Properties
• Z Xform Properties

Table of Laplace and Z Transforms

(Please email me if you find an error)
Using this table for Z Transforms with Discrete Indices
Shortened 2-page pdf of Laplace Transforms and Properties

Entry #	Laplace Domain	Time Domain	Z Domain (t=kT)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Prototype Second Order System (ζ<1, underdampded)
18
19
20

Using this table for Z Transforms with discrete indices

Commonly the "time domain" function is given in terms of a discrete index, k, rather than time.  This is easily accommodated by the table.  For example if you are given a function:

Since t=kT, simply replace k in the function definition by k=t/T.  So, in this case,

and we can use the table entry for the ramp

The answer is then easily obtained