We wake up to the sound of a watch alarm that sounds like this. The sound is a repeated double beep: the duration of each beep is about 200 millisec; the beeping continues for 20 seconds. The frequency is about 1 kilohertz. Occasionally when I am waking up in the morning, I hear it differently. Instead of two beeps, I hear four. I hear one short beep at the beginning of each beep and one short beep at the end. Instead of "beep beep, beep beep" I hear "bee-deep bee-deep, bee-deep bee-deep". Both of us have experienced this doubling at different times. This is not a vague, transient impression. We hear the doubled beeps through several cycles---enough to recognize clearly what we are hearing and to notice that this is not the usual sound. When we hear the doubled beeps, we always have one ear against the pillow. Sometimes we raise our head off the pillow during the beeping. Then the doubling ceases immediately. If we then put our head back down where it was, the doubling does not resume. We never hear the doubling when we are fully awake.

One could readily construct an electronic filter that would produce this anomaly, I believe. The sound one hears is as though the amplitude was modulated with a high-pass filter with a time constant of about 100 milliseconds. (I don't discern any exponential die-off in within one of the double beeps, but that could be because these are very short.)

Possible explanation. One possible way to account for the doubling is to suppose that it is part of an overall sensory filtering process that occurs during sleep. During sleep, one is unaware of most sound (and other stimuli) in the environment. However, some stimuli, like a loud alarm clock, penetrate our consciousness. Our physiology must be tuned to filter out some sounds while preserving others. One simple filter that would admit most sounds requiring waking would be a filter for abrupt sounds---sudden noises. Such a filter would be sensitive to only rapid changes in sound level, such as the beginning or the end of one of the beeps described above. That is, such a filter would account for the anomalous perception reported above.

Implications: Low-level perceptual filtering is commonplace in animal perception. Spatial edge detection and rapid movement detection within the retina of cats and frogs has been well documented. The novelty of the observation reported above is that the filtering is turned on or off depending on the physiological state of the animal. Further, while it is associated with sleep, it does not require unconsciousness: One can simultaneously be awake and also aware of the filtering anomaly. If this mechanism is valid, one might expect analogous filtering to occur with other senses, eg vision or touch. For example a 200 millisecond flash of light would be perceived as two flashes. Further, the doubling should not occur when the onset or decay of the stimulus is gradual rather than abrupt. Thus, if the sound reproduced above were modified so that each beep turned on and off smoothly over 20-50 millisec, one should not hear the doubling anomaly.