**3.9 Discussion**

The bispectral contour matching technique is an extension to the cumulant matching technique. Therefore, the choice of the NN classifier is based on the discussion presented previously. *Prior information* remain as valuable assets and are very much exploited herein. It is the matching of the horizontal 2-d bispectral contours that has been used in the BIC template matching technique instead of the 1-d polar bispectral slices. Because in order to use the 1-d polar bispectrum slices effectively, one needs to use a minimum of 24 polar slices to facilitate capturing the most rapid changes in the bispectrum including null features that could be used as discriminant patterns. Whereas for BIC contours, provided that they are

*Parameters:*The second-order Volterra parameters are: filter length = 6, step-size parameters = 0.005, and 0.0004 for linear and quadratic parts, respectively, delay = 5. The third-order Volterra parameters are: filter length = 6, step-size parameters = 0.001, 0.0002, and 0.0004 for linear, quadratic and cubic parts, respectively, delay = 5. A dual-band-pass filter is applied to the bispectrum, the first has a band- pass of 10 Hz to 20 Hz and the second has a bandpass of 25 Hz to 40 Hz. Optimised Kaiser windows centred at frequencies of 15 Hz, 16 Hz, 17 Hz, 18 Hz, and 19 Hz for the maternal spectrum, and at frequencies of 28 Hz, 29 Hz, 30 Hz, 31 Hz, 32 Hz, 33 Hz, 34 Hz, 35 Hz, 36 Hz, 37 Hz, and 38 Hz for the fetal spectrum are

Classification rate 99.84 100.00

transabdominally-measured ECGs and their respective power spectrum and bispectral

**Se (%)** 

Power spectrum with linearisation 71.29 71.44 34272 34537 71.37

linearisation 87.97 87.46 15048 14436 87.72

synthesiser 88.53 88.04 14352 13764 88.28

synthesiser 90.53 89.73 12324 11364 90.12

The bispectral contour matching technique is an extension to the cumulant matching technique. Therefore, the choice of the NN classifier is based on the discussion presented previously. *Prior information* remain as valuable assets and are very much exploited herein. It is the matching of the horizontal 2-d bispectral contours that has been used in the BIC template matching technique instead of the 1-d polar bispectral slices. Because in order to use the 1-d polar bispectrum slices effectively, one needs to use a minimum of 24 polar slices to facilitate capturing the most rapid changes in the bispectrum including null features that could be used as discriminant patterns. Whereas for BIC contours, provided that they are

Table 3.2. Fetal heart detection quality and classification rate using transabdominallymeasured ECG and their respective power spectrum and bispectral contours with and without linearisation. The total number of fetal heartbeats is 120,000 and the total number of maternal ECG recordings is 30. The performance was assessed against synchronised fetal scalp heartbeats. All mothers were during the first stage of labour at 40 weeks of gestation.

**Sp (%)** 

Table 3.1. The classification rate for the maternal QRS-complex using maternal

**The power spectrum** 

> **FP, out of 120000**

**FN, out of 120000** 

**The bispectrum contours** 

> **Classification rate (%)**

used in both the power spectrum and the BIC.

**Spectral matching template with ANN** 

**Spectral matching template type with and without linearisation using Volterra and in conjunction with** 

Linearised bispectral contour using 2nd

Linearised bispectral contour using 3rd

**classifiers** 

contours.

**ANN classifiers** 

**3.9 Discussion** 

Bispectral contour without

order adaptive LMF Volterra

order adaptive LMF Volterra

horizontally cut at a maximum number of 10 levels, a good quality discriminant picture can be made available for the neural network classifier. For example, it is very unlikely that maxima and troughs are missed because of any changes in their respective positions. Approximately 50,000 maternal cardiac cycles have been included in the analysis. The numbers of bispectral contours compound templates are 10 for the maternal chest, 10 for the fetal scalp, and 140 for the transabdominally-measured 250 msec segments, respectively. Each bispectral compound template is made of 10 horizontal templates at different levels. Starting from a normalised 0 dB and going down in steps of 1 dB each to a – 10 dB.

The maternal transabdominal ECG signal is linearised using an optimised LMF-based secondor third-order Volterra synthesiser. The second-order Volterra synthesiser parameters are: filter length = 6, step-size parameters = 0.005, and 0.0004 for linear and quadratic parts, respectively, delay = 5. The third-order Volterra synthesiser parameters are: filter length = 6, step-size parameters = 0.001, 0.0002, and 0.0004 for linear, quadratic and cubic parts, respectively, delay = 5. The transabdominal ECG signal is segmented into four segments containing; (I) The maternal QRS-complex, (II) the first fetal heartbeat with maternal contribution, (III) QRS-free ECG, and (IV) the second fetal heartbeat with maternal contribution. To segment the transabdominal ECG signals, the window length is carefully chosen to; (i) Yield an acceptable upper threshold of both the deterministic and stochastic noise types inherent in the higherorder statistics of the ECG signals encountered, and (ii) allow the detection of one, two, three, or four fetal heartbeats (FHBs) within one maternal transabdominal cardiac cycle.

The classification procedure starts by matching the bispectral contours of the segments to those of the templates until the first and the second maternal QRS-complexes are detected and their R-waves are pinpointed. The maternal heart rate is accurately calculated from the knowledge of the current and previous R-wave positions. Then, the search for the fetal heartbeat starts at 50 msec before the first maternal R-wave and continues until the second maternal R-wave is reached. Although the ECG bispectral contour template matching technique is very effective in detecting the occurrence of the fetal heartbeats as a whole in the frequency domain even when it is completely buried in noise, it cannot locate the R-wave in the time domain over a window length of 250 msec. However, the maternal heartbeats can be measured fairly accurately and calculate the instantaneous heart rate for the mother. Hence, by counting the number of fetal heartbeats that have occurred between two successive maternal R-waves, one can easily calculate the averaged FHR within the maternal cardiac cycle;

The average FHR = MHR x Number of FHBs / number of maternal heartbeats

the instantaneous maternal heart rate is previously known with some degree of accuracy, and the relative fetal to maternal heartbeat is also known within the maternal cardiac cycle. Hence, the averaged fetal heart rate can be calculated within each maternal cardiac cycle.
