"Gap Tollerancy Formalization in Discrete Signal Processing” FCT, 2012

It is presented a formalization of operational tolerance to lack of data that

may occur in the processing of discrete signals. This research has an empirical

motivation. It was born from problems that arise in processing and analyzing

signals when it is necessary to deal with the lack of knowledge about the signal

values that exist outside the set of available observations.

This text investigates the concept of operation tolerant to missing data,

tolerant to the lack of arguments. It is a defined a symbol for the lack of symbol

and it is alleged that the logic appropriate to handle such situations can not be

the bivalent and must be at least trivalent.

To deal formally with tolerant operations is defined a particular type of

finite set, the urconjunto. Based on this kind of set it is possible to define tolerant

tuple and related norms. One conclusion is that in a tolerant tuple the number of

dimensions can exceed the number of actual components. It is thus possible to

achieve more comprehensive definitions of what is a discrete signal and what are

tolerant operations.

To conclude it is formulated the tolerant generalization for current algebra

and shown some possible lines of inquiry, as the study of probabilities in a

tolerant context.

Keywords: discrete, signal, urset, tolerant, operation.