Event Detection: Qrs-Complexes in Ecg Signals - microLab

BioMedSigProcAnaThe Algorithm: Pre-Processing• let x[n] ˆ= input to and y[n] ˆ= output from pre-processingstage of algorithm• use for pre-processing a linear combination of first- andsecond derivative• first derivative: approximated as absolute value of threepointfirst difference∣y 0 [n] = ∣x[n] − x[n − 2] ∣ .• second derivative: approximated as absolute value of threepointfirst difference of three-point first differences∣y 1 [n] = ∣x[n] − 2x[n − 2] + x[n − 4] ∣ .• output y[n] of pre-processing stage as linear combinationy[n] = 1.3 · y 0 [n] + 1.1 · y 1 [n]To understand the rationals behind the given approximationof the first derivative, we start with a first-difference operator:δ 1 [n] ˆ= x[n] − x[n − 1] •—• ∆ 1 (z) =(1 − z −1) X(z) .6 EventDet 11 2014