Elsevier

Fuzzy Sets and Systems

Volume 79, Issue 2, 22 April 1996, Pages 151-161
Fuzzy Sets and Systems

Sampling, fuzzy discretization, and signal reconstruction

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Abstract

The sampling theorem provides the condition under which a continuous-time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time; it gives a condition for the signal reconstruction problem. The importance of this theorem pertains to the necessity of knowing when a continuous-time signal is uniquely represented by its discrete version, so that continuous-time signals can be properly converted and handled by sampled-data systems like digital computers. The problem of the equivalence between (either continuous-time or discrete-time) signals and their fuzzy descriptions is analyzed here. This encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled-data systems such as fuzzy filters, fuzzy models, or fuzzy controllers. A necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces. Furthermore, a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed. The discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning.

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