Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Tradução, adaptação cultural e propriedades psicométricas da versão brasileira do Short-Form of the Mobility Assessment Tool (MAT-sf)

Objectives: to translate and assess the psychometric properties of the Brazilian short-form of the Mobility Assessment Tool (MAT-sf) in Brazilians community elderly. Methds: the 12 items MAT-sf went through the process of translation and back translation into Portuguese of the Brazil, considering the semantic and cultural adaptation. In a sample of 150 aged 65-74 years living in the community, the instrument's psychometric properties were evaluated by analysis of convergent and construct validity and test-retest reliability. The main outcomes measures used for validation included in the battery of tests of physical ability, self-repor measures of functional limitations, health, depression, cognitive and sex. The test-retest reliability of the instrument was assessed using the intra-class correlation coefficient (ICC), 40 subjects were reassessed after an interval of 14 days of assessment. Results: the concurrent validity for the MAT-sf was evidenced by significant correlations with SPPB (r = 0,53), number of functional limitations (r = -0,62) and depressive symptoms (r = -0,45). The construct validity of the instrument was measured by gradual and significant increase of the MAT-sf scores with high levels of physical performance and with positive self-reported health, also found that MAT-sf scores were statistically differents according to sex. The variation in MAT-sf scores (R2 = 0,41) was explained by SPPB, number of limitations for activities of daily life and depressive symptoms. High values for test-retest reliability was evidencend by ICC = 0,94, 95% CI = 0,90 0,97. Conclusions: the Brazilian version of the short-form of the Mobility Assessment Tool has values of validity and reliability to ensure its use in elderly populations living in communities