A neuromodulator may output stimuli that causes a user to fall asleep faster than the user would in the absence of the stimuli. Alternatively, the stimuli may modify a sleep state or behavior associated with a sleep state, or may cause or hinder a transition from a waking state to a sleep state or from a sleep state to another sleep state. The neuromodulator may take electroencephalography measurements. Based on these measurements, the neuromodulator may detect, in real time, instantaneous amplitude and instantaneous phase of an endogenous brain signal. The neuromodulator may output stimulation that is, or that causes sensations which are, phase-locked with the endogenous brain signal. In the course of calculating instantaneous phase and amplitude, the neuromodulator may perform an endpoint-corrected Hilbert transform. The stimuli may comprise auditory, visual, electrical, magnetic, vibrotactile or haptic stimuli.