Apparatus and methods for monitoring electrical activity within the brain of a person (“brainwaves”) employing electrodes or other sensors placed proximate to portions of the body below the head to develop raw signals without physically touching the body and penetrating hair and clothing. Additionally, apparatus and methods for monitoring electrical activity within the brain of a person (“brainwaves”) employing non-contacting sensors placed proximate to portions of the head to develop raw signals. The raw signals are filtered to produce analysis signals including frequency components relevant to brain electrical activity while attenuating unrelated frequency components. The apparatus and methods can be used for biofeedback-based attention training, human performance training, gaming, biometrics, cognitive state detection, and relaxation training. Either wired or wireless signal connections are made to electronic circuitry, typically including a digital computer, for performing signal processing and analysis functions.