Thesis - Instituto de Telecomunicações

4.2. ELECTRODERMAL ACTIVITY 77t 3 = 6 b ). f(t) =at 4 e −bt u(t), (4.36)f ′ (t) = (4 − bt)at 3 e −bt u(t), (4.37)f ′′ (t) = (bt − 2)(bt − 6)at 2 e −bt u(t). (4.38)The proposed base model for a singular SCR event is based on the generalization ofequation 4.36 by considering t 0 ≠ 0, leading to the time and transfer function representations:h(t) =f(t − t o )u(t − t o )=a(t − t 0 ) 4 e −b(t−t0) u(t − t o ), (4.39)aH(s) = 4!(s + b) 5 , (4.40)where a is a measure of event amplitude. The total EDA signal, f EDA , is modeled by thesum of the SCR with a constant representing the SCL:f EDA (t) =h(t)+c. (4.41)SCR Detection and Model-FittingThe overall procedure of model fitting and SCR detection and quantification is based onsignal filtering and computation of signal derivatives. Since signal derivation eliminatesconstant components, we can for the moment forget the SCL component, which may beconsidered as equivalent to zero. The SCL value can be easily computed as a final step ofthe method, as shown later.As summarized by the pseudo-code in algorithm 1, the processing steps, required todetect and fit the proposed EDA model to a collected signal, are:Signal filtering First, the signal is filtered with a low pass filter with cutoff frequency 5Hz,in order to remove high frequency noise. The first and second order derivatives arecomputed based on the samples differences (see equation 4.42, where e is the sampledand filtered EDA signal, and ∆t is the sampling period).e ′ t = e t − e t−1,e ′′t∆t= e′ t − e ′ t−1. (4.42)∆t