Using this chart, you can see how to convert among linear system representations. It shows how to convert …

- a linear continuous-time system into a linear discrete-time system
- between an impulse response model and a frequency response model
- between a differential equation and an impulse response model
- between the s-domain and a frequency response model
- between the s-domain and differential equations
- between difference equations and differential equations
- and more!

Once you see how these representations are all interchangeable, it is easy to see how to reuse the different tools, which are usually specific to a given representation.

The continuous-time models and equations for conversion are shown below.

This entry answers the following questions (and more…):

- How to convert an s-domain model into a differential equation.
- How to convert a transfer function into a differential equation.
- How to convert an impulse response into a differential equation.
- How to convert an impulse response into a frequency response.
- How to convert an impulse response into a transfer function.
- …..

All text and images are release under the Creative Commons Attribution 3.0 License as long as this blog and the author (Ed Tate) are attributed.