Basic Concepts of Interval Digital Signal Processing
Roque Mendes Prado Trindade, C. Bedregal · 2010
Abstract—Interval mathematics has been used in Signal Processing as a tool for representing uncertainties that arise from finite numeric representation, limited precision sensors and the quantization process. In some control systems, such as soft computing or forecast systems, the uncertainties are a consequence of variable instability, signal variance, or the safety rate of some actuators. Papers with specific applications in this area have been published, but few have dealt with the theoretical foundation of interval mathematics applied to signal processing. This essay is a starting point on interval mathematics in the foundation of signal processing. It is an analytical approach for dealing with interval linear systems with an application perspective in signal processing. Interval linear systems will be used as mathematical models in real systems representation, where the intervals represent the uncertainty of the system. In this approach only linear and time invariant systems with single input and single output (SISO) are used. For this purpose the classical basic properties of real linear systems will be extended. These properties are: causality, stability, additivity and homogeneity. Finally, an interval convolution definition is proposed to represent uncertainty systems and signals more accurately; it is also an important tool for digital signal processing.