Different Synthesis Methods

There are several methods for synthesising RII filters, depending on the criteria imposed;

  • Imposed temporal response.

- Impulse response  \(\rightarrow\) Impulse invariance method

- Index response  \(\rightarrow\) Index invariance method

  • Numerical simulation of a differential equation

- Euler method

- Trapezoid method

  • Imposed frequency response: Bilinear transformation

In these methods, we seek to create a digital filter from an analogue filter, a prototype transfer function. \(G_{anal}\left(p\right)=\frac{1}{1+\tau p}\) with \(\tau=T_e\).