October 2006
Intermediate to advanced
369 pages
8h 11m
English
Content preview from Digital Filters Design for Signal and Image Processing
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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 
:
| – 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 ...