Fetal echocardiography is an operator-dependent examination technique requiring a high level of expertise. Pulsed-wave Doppler (PWD) is often used as a reference for the mechanical activity of the heart, from which several quantitative parameters can be extracted. These aspects suggest the development of software tools that can reliably identify complete and clinically meaningful fetal cardiac cycles that can enable their automatic measurement. Several scientific works have addressed the tracing of the PWD velocity envelope. In this work, we assess the different steps involved in the signal processing chains that enable PWD envelope tracing. We apply a supervised classifier trained on envelopes traced by different signal processing chains for distinguishing complete and measurable PWD heartbeats from incomplete or malformed ones, which makes it possible to determine the impact of each of the different processing steps on the detection accuracy. In this study, we collected 43 images and labeled 174,319 PWD segments from 25 pregnant women volunteers. By considering seven envelope tracing techniques and the 23 different processing steps involved in their implementation, the results of our study reveal that, compared to the steps investigated in most other works, those that achieve binarisation and envelope extraction are significantly more important (p < 0.05). The best approaches among those studied enabled greater than 98% accuracy on our large manually annotated dataset.