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Brain Computer Interface (BCI) is gaining popularity due to recent advances in developing small and compact electronic technology and electrodes. Miniaturization and form factor reduction in particular are the key objectives for Body Sensor Networks (BSNs) and wearable systems that implement BCIs. More complex signal processing techniques have been developed in the past few years for BCI which create further challenges for form factor reduction. In this paper, we perform a computational profiling on signal processing tasks for a typical BCI system. We employ several common feature extraction techniques. We define a cost function based on the computational complexity for each feature dimension and present a sequential feature selection to explore the complexity versus the accuracy. We discuss the trade-offs between the computational cost and the accuracy of the system. This will be useful for emerging mobile, wearable and power-aware BCI systems where the computational complexity, the form factor, the size of the battery and the power consumption are of significant importance. We investigate adaptive algorithms that will adjust the computational complexity of the signal processing based on the amount of energy available, while guaranteeing that the accuracy is minimally compromised. We perform an analysis on a standard inhibition (Go/NoGo) task. We demonstrate while classification accuracy is reduced by 2%, compared to the best classification accuracy obtained, the computational complexity of the system can be reduced by more than 60%. Furthermore, we investigate the performance of our technique on real-time EEG signals provided by an eMotiv® device for a Push/No Push task.