Delay accuracy in bat sonar is related to the reciprocal of normalized echo bandwidth, or Q.

Big brown bats (Eptesicus fuscus) emit wideband, frequency-modulated biosonar sounds and perceive the distance to objects from the delay of echoes. Bats remember delays and patterns of delay from one broadcast to the next, and they may rely on delays to perceive target scenes. While emitting a series of broadcasts, they can detect very small changes in delay based on their estimates of delay for successive echoes, which are derived from an auditory time/frequency representation of frequency-modulated sounds. To understand how bats perceive objects, we need to know how information distributed across the time/frequency surface is brought together to estimate delay. To assess this transformation, we measured how alteration of the frequency content of echoes affects the sharpness of the bat's delay estimates from the distribution of errors in a psychophysical task for detecting changes in delay. For unrestricted echo frequency content and high echo signal-to-noise ratio, bats can detect extremely small changes in delay of about 10 ns. When echo bandwidth is restricted by filtering out low or high frequencies, the bat's delay acuity declines in relation to the reciprocal of relative echo bandwidth, expressed as Q, which also is the relative width of the target impulse response in cycles rather than time. This normalized-time dimension may be efficient for target classification if it leads to target shape being displayed independent of size. This relation may originate from cochlear transduction by parallel frequency channels with active amplification, which creates the auditory time/frequency representation itself.