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Digital Filters Design for Signal and Image Processing by Mohamed Najim

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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 images:

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

Here are the three subsets of images:

The open unit disk images
The closed unit disk images
- The unit circle images

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

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