Vital signals provide essential information regarding the health status of individuals, thereby contributing to health management and medical research. Present monitoring methods, such as ECGs (Electrocardiograms) and smartwatches, demand proximity and fixed postures, which limit their applicability. To address this, Non-contact vital signal measurement methods, such as CW (Continuous-Wave) radar, have emerged as a solution. However, unwanted signal components and a stepwise processing approach lead to errors and limitations in heart rate detection. To overcome these issues, this study introduces an integrated neural network approach that combines noise removal, demodulation, and dominant-frequency detection into a unified process. The neural network employed for signal processing in this research adopts a MLP (Multi-Layer Perceptron) architecture, which analyzes the in-phase and quadrature signals collected within a specified time window, using two distinct input layers. The training of the neural network utilizes CW radar signals and reference heart rates obtained from the ECG. In the experimental evaluation, networks trained on different datasets were compared, and their performance was assessed based on loss and frequency accuracy. The proposed methodology exhibits substantial potential for achieving precise vital signals through non-contact measurements, effectively mitigating the limitations of existing methodologies.