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The Chirp Radar Theory
Figure 4B illustrates the principle of pulse compression for a chirp radar receiver in the 1960s, which was based on analog electronics, not digital methods (as in Figure 4A). The broad- cast signal sweeps from high frequency to low frequency, and the receiver breaks the entire frequency span of the sweep into multiple, closely-spaced frequency channels using band-pass filters. It imposes an electronic delay on each frequency in in- verse relation to its place in the sweep. The highest frequencies are delayed the longest, the middle frequencies are delayed less long, and the lowest frequencies are delayed the least. As a result, the frequencies all emerge from the receiver’s paral- lel delay elements at the same instant in time to form a com- pressed pulse. In this scheme, the receiver contains a frozen time-reversed template of the FM sweep (a time-frequency template; Figure 4B) instead of a time-reversed impulse re- sponse (a time-amplitude template; Figure 4A).
The 1960s-era chirp radar theory is an extension of the spec- trogram theory of Griffin and Galambos (see Griffin, 1958) into how the spectrograms might actually be processed to achieve very sharp delay registration. The segmentation of frequencies with band-pass filters before applying different delays in a chirp radar receiver resembles the segmentation of frequencies by the parallel, frequency-tuned receptors and auditory nerve cells of the mammalian cochlea (inner ear), a fact known by that time (von Békésy, 1960).
Advent of Neurophysiology
A crucial part of the original evidence for the existence of echolocation was the finding that the cochlea of the bat re- sponded to the same ultrasonic frequencies that were present in the sounds the bat emitted. This inaugurated an intensive neurophysiological research effort that has now spanned many decades and constitutes the larger part of published work (Neuweiler, 2000; Surlykke et al., 2014; Fenton et al., 2016). The salient discoveries specific to echolocation theory were that (1) neural responses to the second of two sounds, the “echo,” recovered swiftly and strongly from the effects of the first sound, the “broadcast,” clarifying that bats are not in fact at a disadvantage when listening for echoes that follow broadcasts; (2) middle ear attenuation of broadcasts preced- ed auditory transduction of broadcasts by the inner ear, so that sensitivity to the emitted sound is substantially reduced while sensitivity to echoes recovers in a graded fashion; (3) neural responses at successive levels of the bat’s auditory system incorporate additional neural gain control for fur- ther reducing responses to broadcasts in favor of echoes; (4) neurons at all levels of the bat auditory system are tuned to
specific frequencies somewhere in the range of echolocation sounds, thus confirming that cochlear frequency tuning and subsequent tonotopic representation encode the FM sweeps of echolocation sounds; and (5) the action of neurons in the bat’s auditory system to short-duration FM sounds that mimic echolocation signals are restricted almost entirely to single-spike, phasic-on responses.
The Neural Spectrogram Code
Segmentation of FM sweeps into numerous, parallel fre- quency-tuned neural channels is the auditory system’s way to create spectrograms. Individual auditory receptors and then individual neurons at all levels of the bat’s auditory system (in the brain) are tuned to specific frequencies, accompanied by clear topographic mapping of frequency that mimics the cochlea’s frequency map. When the acoustic stimuli are brief FM sweeps that mimic echolocation broadcasts and echoes, the vast majority of neurons in the bat’s cochlear nucleus (the first stage of auditory neural processing in the brain), the inferior colliculus (the principle neural integrating cen- ter in the auditory pathway), and the auditory cortex (the highest stage of neural processing and, in effect, a kind of display) react with an average of just one neural action po- tential (“spike”) for each sound (phasic-on response; Pollak and Casseday, 1989). This representation is a time-frequency point process, an auditory spectrogram. In physiological terms, auditory computations based on frequency consist largely of local inhibitory connections between neighboring frequency channels that feed forward to sharpen the regis- tration of frequency and create responses that are selective for downward or upward FM sweeps at different sweep rates and long-distance facilitatory connections that link widely separated frequency channels tuned to harmonic frequencies (e.g., 1st harmonic with 2nd harmonic) to create responses that require the simultaneous presence of both harmonics.
To carry out computations on spike timing, the spikes have to be arranged at different latencies in different neurons. Spikes that occur at short latencies have to be preserved, remem- bered, so that they can be made available to compare with spikes that occur later. The problem with a single-spike code is that once a spike has occurred, the information it conveys evaporates. Having an auditory memory for the timing of single spikes means repeating that spike in different neurons at progressively longer latencies to carry its information for- ward so it will be available at a later time when it is needed. The particular details of latency registration are crucial for understanding auditory computations in biosonar (Sim- mons and Simmons, 2010; Simmons, 2012, 2014).
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