Transient responses to tone bursts

Investigating theoretical conditions under which linearly-operating tuned structures produce click-like transient responses to onsets and offsets of trapezoidal tone bursts, we come to the following conclusions: (1) each of the four corners of the trapezoidal tone burst is capable of eliciting such a response; (2) the amplitude of the response and its dependence on the frequency of the modulated tone both depend on the phase of the modulated sinusoid at the time a corner occurs; (3) such responses will arise in structures having sufficiently steep band edges, provided that the frequency of the modulated tone is well outside the pass band of the structure--for a corner in cosine phase, the sustained slope of the low-frequency band edge must be greater than zero and that of the high-frequency band edge must be greater than 12 dB/Oct, for a corner in sine phase the sustained slope of the low-frequency band edge must be greater than 6 dB/Oct and that of the high-frequency band edge must be greater than 18 dB/Oct; (4) they will not arise in response to tone bursts whose frequencies fall within the pass band of the structure; (5) nor will they arise in response to a trapezoidal tone burst of any frequency applied to structures (such as simple microphones or drivers) following second-order dynamics and having both spectral zeros at infinity. We present theoretically derived relationships between the amplitude of transient responses and the tone-burst frequency, not only for the corners of trapezoidal tone bursts, but also for tone bursts of more general shapes. We conclude that, owing to its extraordinarily steep high-frequency rolloff, the filter associated with each cochlear axon is well suited to extracting temporal information from onset or offset singularities in modulated tones whose frequencies are above the characteristic frequency of the filter. Applying the theory to observed onset and offset responses to high-intensity tone bursts in auditory afferents of the Mongolian gerbil, we conclude that some of the responses we observed must have been sculpted in part by cochlear nonlinearities.