Event Detection: Qrs-Complexes in Ecg Signals - microLab

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BioMedSigProcAnaThis filter has a zero at z = 1—at Dc frequency—and has amagnitude response of 2 sin(ˆω/2). For sufficiently low frequenciesˆω, it approximates the derivative operation as we see from2 sin(ˆω/2) ≈ 2ˆω/2 = ˆω. To obtain a smoothing such that highfrequencynoise is not too much amplified, we post-process thesequence δ 1 [n] by a two-point moving-average filter having transferfunction (1 + z −1 ): 1ỹ 0 [n] ˆ= δ 1 [n] + δ 1 [n − 1]= ( x[n] − x[n − 1] ) + ( x[n − 1] − x[n − 2] )= ( x[n] − x[n − 2] ) .In the z-transformation domain we equivalently haveỸ 0 (z) ===(1 + z −1) ∆ 1 (z)(1 + z −1)( 1 − z −1) X(z)(1 − z −2) X(z) .Clearly, the complete filter (1 − z −2 ) has one zero at z = 1—atfrequency ˆω = 0—, which approximates the derivative, and asecond zero at z = −1—at frequency ˆω = ±π—, which suppresseshigh frequency noise. The magnitude response of the filteris 2 sin(ˆω); for low frequencies we again have 2 sin(ˆω) ≈ 2ˆω,which approximates a derivative with a gain 2.For the approximation of the second derivative consider thesequence ỹ 0 [n] being the output of a three-point first differencefilter: ỹ 0 [n] = x[n] − x[n − 2]. Processing this sequence by1 We denote the output of this processing step by ỹ 0 [n] to distinguish itfrom y 0 [n], which we use in the slide on page 11, and which is the absolutevalue of ỹ 0 [n].6 EventDet 12 2014
BioMedSigProcAnaanother three-point first difference filter, we obtain 2ỹ 1 [n] ˆ= ỹ 0 [n] − ỹ 0 [n − 2]= ( x[n] − x[n − 2] ) − ( x[n − 2] − x[n − 4] )= ( x[n] − 2x[n − 2] + x[n − 4 ) .The Algorithm: Decision Rule• threshold y[n] ˆ= output of pre-processing with a thresholdvalueof 1.0• if y[n 0 ] ≥ 1.0 for a certain n 0 , then compare next 8 samplesto threshold• if 6 or more of these 8 samples pass threshold test, thentake the 8-samples segment as part of a Qrs complex• advantage: additionally to detecting Qrs complexes, thealgorithm produces a pulse that is proportional in widthto the Qrs complex• disadvantage: the method is extremely sensitive to highfrequencynoise2 Again, we denote the output of this processing step by ỹ 1 [n] to distinguishit from y 1 [n], which we use in the slide on page 11, and which is theabsolute value of ỹ 1 [n].6 EventDet 13 2014
Page 4 and 5: BioMedSigProcAnaExamples of Events:
Page 6: BioMedSigProcAnaDetector-Critical T
Page 10: BioMedSigProcAnaQrs Detection as an
Page 13: BioMedSigProcAnaThe Algorithm: Pre-
Page 17 and 18: BioMedSigProcAnademand on preservat
Page 19 and 20: BioMedSigProcAnaSimple Example (con
Page 21 and 22: BioMedSigProcAnawhereas the form (1
Page 23 and 24: BioMedSigProcAnaSimple Example (con
Page 25 and 26: BioMedSigProcAnasee our exemplifyin
Page 27 and 28: BioMedSigProcAnaExample: Zeros for
Page 29 and 30: BioMedSigProcAnaGeneral: Transfer F
Page 31 and 32: BioMedSigProcAnaWe present the algo
Page 33 and 34: BioMedSigProcAnaBandpass Filter: Th
Page 37 and 38: BioMedSigProcAnawhich delays each s
Page 41 and 42: BioMedSigProcAnarealized highpass f
Page 43 and 44: BioMedSigProcAnafrom the delayed in
Page 45 and 46: BioMedSigProcAnafrequency of ˆω r
Page 47 and 48: BioMedSigProcAnaThe Derivative Oper
Page 49 and 50: BioMedSigProcAnaThe Moving-Window I
Page 51 and 52: BioMedSigProcAnaWe also note that i
Page 53 and 54: BioMedSigProcAnaSampling-Rate Conve
Page 55 and 56: BioMedSigProcAnathat is, the moving
Page 57 and 58: BioMedSigProcAnato a Cic-filter str
Page 59 and 60: BioMedSigProcAna[Goe14b] Josef Goet

Event Detection: Qrs-Complexes in Ecg Signals - microLab

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