Digital Filters Design for Signal and Image Processing

11.2. Stability criteria

In this section, we will pre sent different stability criteria for causal and semi-causal recursive filters. A stability criterion is a sufficient and necessary condition to assure BIBO stability.

We start by introducing three subsets of :

– The open unit bidisk
– The closed unit bidisk
– The unit bi-circle or toric unit

Here are the three subsets of :

– The open unit disk
– The closed unit disk
- The unit circle

Let us consider a continuous function : that does not vanish in the closed unit bidisk. It results from the continuity of |f| and the ...