Missing Data
"Gap Tollerancy Formalization in Discrete Signal Processing” FCT, 2012
Author: Raul Tello Rato Supervisor: Manuel Ortigueira AbstractIt 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.