Fetal heart rate estimation by fitting half-wave rectified cosine functions to power spectra of fetal ecg waveforms

In this paper, we consider the fundamental period estimation problem for fetal ECG waveforms. In our previous paper, we established a new fundamental period estimator based on the minimization of a cost function which measures the differences between the discrete Fourier transform (DFT) of a fetal ECG waveform and the DFTs of its circularly shifted forms. We showed that the minimization of this cost function is equivalent to finding the cosine waveform which matches best to the ECG power spectrum. In other words, the Euclidean inner product between the optimal cosine waveform and the ECG power spectrum yields the largest value. The negative cycles of regular cosine waveforms cause some mismatch with the ECG power spectrum since the power spectrum has only nonnegative values. In order to deal with this problem, in this paper, we fit half-wave rectified cosine waveforms to the ECG power spectrum since rectified cosine waveforms have also only nonnegative values. With two examples, we demonstrate that this method achieves very accurate estimates for both synthetic and real fetal ECG waveforms when compared to the well-known generalized correlation method and the method with regular cosine waveforms.