On robust detection of brain stimuli with Ramanujan Periodicity Transforms

Pouria Saidi, George K. Atia, Azadeh Vosoughi

Abstract: Visual Evoked Potentials (VEPs) are the brain responses to repetitive visual stimuli. The ability to detect the underlying frequencies of VEPs is crucial to advancing Brain Computer Interfaces (BCIs). This paper considers the detection of such frequencies using a Ramanujan Periodicity Transform based model. We analyze the performance of a generalized likelihood ratio detector and derive the exact distributions of the sufficient statistics under hypotheses corresponding to different stimulus frequencies using confluent hyper-geometric functions, along with flexible approximate distributions. Choosing stimulation periods with non-overlapping divisors is shown to enhance the detection performance. Our analysis provides guidelines for efficient design of stimulus waveforms for BCIs.