This paper proposes the novel Sleep Apnea Syndrome (SAS) detection method based on the frequency analysis of the overnight bio-vibration data acquired from mattress sensor. Concretely, this paper designs the index called Degree of Convexity of the Logarithmic Spectrum (DCLS), which quantifies the degree of convexity by computing the difference between the waveform of the averaged logarithmic spectrum and the waveform of its approximation formula, and employs it to detect SAS. Through the human subject experiment on the SAS detection, the following implications have been revealed: (1) the SAS subjects tend to have the large density around 3Hz, and the average of DCLS in SAS subjects and healthy subjects are 98.6±10.1 and 48.2±6.8 respectively, which succeeds to correctly separate the nine SAS subjects and the nine healthy subjects; and (2) the characteristics of the WAKE stage are different between the SAS and healthy subjects.