An FFT-based algorithm for Obstructive Sleep Apnea (OSA) patient identification using R-R interval (RRI) data is investigated. The identification is done on the whole record as OSA patient or non-patient (normal). The power spectral density of the three main bands of the RRI data is computed and then three identification factors are calculated from their ratios. The first identification factor is the ratio of the PSD of the low-frequency (LF) band to that of the high-frequency (HF) band. The second identification factor is the ratio of the PSD of the very low-frequency (VLF) band to that of the low-frequency (LF) band, while the third identification factor is the ratio of the PSD of the very low-frequency (VF) band to that of the high-frequency (HF) band. The RRI data used in this work were drawn from MIT database. The three identification factors are tested on MIT trial data. The best factor, which is the (VLF/LF) PSD ratio, is then tested on MIT test data and to evaluate the performance of the identification. The efficiency of identification approaches 87%. The method is then improved by applying FFT on short records and averaging the results to get an efficiency of 93%. Another improvement was done by zero-padding the short records to double its size and then averaging the results to get an efficiency of 93%. This efficiency is compared with a previous work on the same purpose using wavelets which resulted in 90 % accuracy.