A least square DFT method for sub-sample fetal heart rate estimation under noisy conditions

In this paper, we consider fundamental period estimation problem for fetal ECG waveforms. By means of a signal separation algorithm, a fetal ECG waveform can be obtained from abdominal ECG of a pregnant woman which contains both maternal and fetal ECG waveforms. We develop a new fundamental period estimator based on minimization of a cost function which measures the least square differences between the discrete Fourier transform (DFT) of the original fetal ECG waveform and the DFT of its circularly shifted form. This cost function attains to its minimum when the circular shift corresponds to integer multiples of the fundamental period. We minimize this cost function to obtain an integer fundamental period estimate. We also minimize this cost function with a gradient descent method to achieve sub-sample precision in fundamental period estimation. With two examples, we demonstrate applications of this method to fetal ECG waveforms and compare its performance to the well-known generalized correlation method.