**3.3 Typical examples of bispectra and their contours**

Linearisation is a key step in the signal processing and it is applied using an optimised third-order Volterra synthesiser to all the results included. Fig. 3.1 depict dual-band-pass filtered bispectra and their contours normalised to the maternal QRS-complex spectral peak for the transabdominally-measured ECG segments I, II, III, and IV. Segment I: predominantly maternal QRS-complex, segment II: the first fetal heartbeat with maternal contribution; segment III: QRS-free ECG, and segment IV: the second fetal heartbeat with maternal contribution. The dual-band-pass filter consists of two fifth-order Butterworth filters with cut-off frequencies of 10 Hz to 20 Hz, and 25 Hz to 40 Hz, respectively, a passband attenuation of 0.5 dB, and a stop-band attenuation larger than 70 dB. The sampling rate is 500 Hz. Optimised Kaiser weighting coefficients are used for the fetal and maternal ECGs to enhance their spectral peaks at 30 Hz and 17 Hz, respectively. The Kaiser windows are centred at frequencies of 15 Hz, 16 Hz, 17 Hz, 18 Hz, and 19 Hz for the maternal QRS-complex, 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 heartbeat.

Fig. 3.1 (I) shows the maternal QRS-complex principal bispectral peaks and contours centred at the frequency pairs (18 Hz, 5 Hz) and (18 Hz, 16 Hz). These maternal frequency pairs with a frequency peak at 18 Hz slightly deviate from the actual frequency of 17 Hz (Rizk et al., 2000), which is due to the BIC bias. The maternal optimised Kaiser window centred at 18 Hz will help to detect this deviated peak. Fig. 3.1 (II) shows the first fetal heartbeat principal bispectral peaks and contours at the frequency pairs (30 Hz, 5 Hz), (30 Hz, 18 Hz), and (30 Hz, 30 Hz). The fetal optimised Kaiser window centred at 30 Hz will help to detect these peaks. Note that these peaks are sharp. Fig. 3.1 (III) shows the QRS-free ECG bispectral peak and contours centred at the frequency pair (27 Hz, 15 Hz). Note that the BIC of the QRS-free ECG is at approximately -12 dB which is 3 dB and 6 dB lower than that of the first and second fetal heartbeats, respectively. Fig. 3.1 (IV) shows the second fetal heartbeat principal bispectral peak and contours centred at the frequency pairs (30 Hz, 5 Hz), and (30 Hz, 28 Hz). The fetal optimised Kaiser window centred at 30 Hz will help to detect these peaks.
