Bilinear Transform (Tustin's Method) applied to the Derivative

1. What is the formula for Tustin transformation?
2. What is bilinear transformation method?
3. What are the applications of bilinear transformation?
4. What is the Tustin approximation?

What is the formula for Tustin transformation?

For example, applying the Tustin transform at frequency σ0 = 1 to H(z) = 1/z yields G(s) = (1 − s)/(1 + s).

What is bilinear transformation method?

The bilinear transformation is a mathematical mapping of variables. In digital filtering, it is a standard method of mapping the s or analog plane into the z or digital plane. It transforms analog filters, designed using classical filter design techniques, into their discrete equivalents.

What are the applications of bilinear transformation?

The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.

What is the Tustin approximation?

Absfract-The Tustin approximation is a simple way for determina- tion of a discrete-time representation of a continuous-time control system and is sufficiently precise, if a sampling interval is chosen properly.