In the present study, "obstructive sleep apnea (OSA) patients" and "non-OSA patients" were classified into two groups using with two synchronic heart rate variability (HRV) series obtained from electrocardiography (ECG) and photoplethysmography (PPG) signals. A linear synchronization method called cross power spectrum density (CPSD), commonly used on HRV series, was performed to obtain high-quality signal features to discriminate OSA from controls. To classify simultaneous sleep ECG and PPG signals recorded from OSA and non-OSA patients, various feed forward neural network (FFNN) architectures are used and mean relative absolute error (MRAE) is applied on FFNN results to show affectivities of developed algorithm. The FFNN architectures were trained with various numbers of neurons and hidden layers. The results show that HRV synchronization is directly related to sleep respiratory signals. The CPSD of the HRV series can confirm the clinical diagnosis; both groups determined by an expert physician can be 99% truly classified as a single hidden-layer FFNN structure with 0.0623 MRAE, in which the maximum and phase values of the CPSD curve are assigned as two features. In future work, features taken from different physiological signals can be added to define a single feature that can classify apnea without error.