In a psychophysical task with echoes that jitter in delay, big brown bats can detect changes as small as 10-20 ns at an echo signal-to-noise ratio of approximately 49 dB and 40 ns at approximately 36 dB. This performance is possible to achieve with ideal coherent processing of the wideband echoes, but it is widely assumed that the bat's peripheral auditory system is incapable of encoding signal waveforms to represent delay with the requisite precision or phase at ultrasonic frequencies. This assumption was examined by modeling inner-ear transduction with a bank of parallel bandpass filters followed by low-pass smoothing. Several versions of the filterbank model were tested to learn how the smoothing filters, which are the most critical parameter for controlling the coherence of the representation, affect replication of the bat's performance. When tested at a signal-to-noise ratio of 36 dB, the model achieved a delay acuity of 83 ns using a second-order smoothing filter with a cutoff frequency of 8 kHz. The same model achieved a delay acuity of 17 ns when tested with a signal-to-noise ratio of 50 dB. Jitter detection thresholds were an order of magnitude worse than the bat for fifth-order smoothing or for lower cutoff frequencies. Most surprising is that effectively coherent reception is possible with filter cutoff frequencies well below any of the ultrasonic frequencies contained in the bat's sonar sounds. The results suggest that only a modest rise in the frequency response of smoothing in the bat's inner ear can confer full phase sensitivity on subsequent processing and account for the bat's fine acuity or delay.