Introduction

The objective is to convert an analogueue filter into a digital filter, with the latter serving as an approximate design of the ideal analogueue filter. However, certain inevitable drawbacks need to be constrained in this transformation. We anticipate oscillations in both the passband and the attenuated band of the filter, with a transition band forming between these two bands.

Figure 7 : Analogue Filter with Oscillations.

The most commonly used synthesis methods rely on the properties of analogueue filters, starting with a prototype analogueue transfer function filter \(G(p)\) with the desired characteristics. Then, we seek the digital transfer function filter Hnum(z) having substantially the same properties:

  • Same impulse response

  • Same-step response

  • Same frequency response over the interval \(\left[-\frac{f_e}{2},\ \frac{f_e}{2}\right]\)