Abstract-This paper proposes to decompose the maternal transabdominal ECG signal into its linear, quadratic and cubic parts and retain only the linear part for further signal processing. The synthesiser will model the quadratic and cubic parts of the transabdominal ECG signal. This is done by predicting each sample of the maternal transabdominal full cardiac cycles. In order to linearise (retain the linear part and remove the quadratic and cubic parts) ECG signals, non-linear structures should be utilised. This paper proposes to linearise the fetal scalp electrode, the maternal chest, and the maternal transabdominal ECG signals using adaptive least-mean-square (LMS) and least-mean-fourth-based (LMF), quadratic and cubic Volterra structures.