Thesis - Instituto de Telecomunicações

74 CHAPTER 4. SIGNAL PROCESSING AND FEATURE EXTRACTIONFigure 4.4: Synthetic SCR with first and second order derivatives and the respective zerosmarked.speed of rise until the maximum value is achieved at t 2 (the second instant where SC ′ = 0).The decay zone starts, and passes a notable point where the decreasing speed slows at t 3(the second instant where SC ′′ = 0). After this, the signal continues to decrease to zero,without any other relevant occurrences.From figure 4.4, and based on empirical evidence, we note that the signal is continuouslydifferentiable, and that the four temporal marks (t 0 ,t 1 ,t 2 ,t 3 ) are approximately evenlyspaced in time:t 1 − t 0 ≃ t 2 − t 1 ≃ t 3 − t 2 . (4.26)In section 4.2.3 we validate this statement based on experimental results on a set of realdata signal acquisition in the context of a cognitive task.In order to give a mathematical formulation to the SCR, obeying the observed characteristicsof the signal expressed in equation 4.26, we considered a simple representation of