A comprehensive computational model of animal biosonar signal processing
Fig 4
Algorithms in SCAT model for processing of FM pulses.
(A) Initial reception of biosonar broadcast and returning echo. The FM pulse contains two harmonic sweeps FM1, FM2) and is followed 6 ms later by 100-μs two-glint FM echoes containing multiple interference nulls at frequencies 10 kHz apart (reciprocal of 100-μs glint spacing) caused by overlapping glint reflections. The model computes spectrograms with 161 parallel gammatone bandpass filters tuned to center frequencies of 20–100 kHz. Filter outputs are half-wave rectified, lowpass-filtered at 10 kHz, and thresholded with 10 amplitude levels. In each channel, the time that elapses between crossings from the same threshold in the chirp and the echo (horizontal arrows, blue circles) marks delay measurements. At frequencies where echo and broadcast spectrograms have the same amplitude, crossings register echo delay from times-of-occurrence accurately. If the echo is weaker, crossings across all frequencies are later due to amplitude-latency trading, and the delay estimate is longer. At frequencies with interference nulls, echo amplitude is locally weaker than at surrounding peak frequencies. At nulls, crossing is later due to amplitude-latency trading (red time offset). (B) Delay is estimated frequency-by-frequency using the pulse-to-echo elapsed times. Threshold crossings in the pulse mark the start of the delay estimate (time zero). Across frequencies, time intervals between pulse and echo crossings are aligned on pulse thresholds at zero time, which dechirps the FM sweeps to make vertical row of time marks. Only crossings from one threshold are shown in A and B to illustrate time marks (blue circles). Time of echo thresholds creates a similar vertical row of marks in each channel, modified by amplitude-latency trading. The threshold marks at the nulls occur later (to the right), causing the dechirped echo to have a scalloped appearance. The leftmost, leading edge of the curved thresholds marks the echo’s 6 ms delay. (C) Inversion of representation from echo amplitudes across frequencies to echo nulls across frequencies. Close-up view on left shows dechirped echo threshold marks for 6–7 activated thresholds (#1 up to 7 out of 10 levels on color bar). This representation is densely populated, coming from all the time-frequency values that exceed different threshold levels spread across about 0.2 ms from lowest threshold (dark blue) to highest threshold (light green). Spectrogram amplitudes track along the thresholds as clusters where they exceed thresholds; nulls have marks only at lowest thresholds because their amplitudes are weak (dark blues), and the track of these threshold events is curved, extending to longer times (rightward) due to amplitude-latency trading. Between peaks, where the thresholds are clustered, there are voids at the center of nulls where none of the thresholds are crossed. Locations of nulls are extracted from scalloped pattern of thresholds across frequencies. These longer latencies and the voids are transformed into representation of the nulls (red horizontal arrows), which is a sparse representation due to inversion from the dense representation of amplitudes that exceed thresholds. This peak-to-null inversion is key to subsequent processing: The late or absent responses at nulls trigger new responses that progress to next stage, a triangular network of model neurons that registers the nulls and connects adjacent nulls with triangular connections at different frequency spacings set by frequency separation between filters in the filterbank. Frequencies of nulls are marked in red dots at the left of the triangular network in 0.5 kHz frequency steps, the same as the gammatone filters. The frequency differences between nulls form a zig-zag pattern of coincidence responses that register the frequency spacing of adjacent nulls (Δf) by their right-most triangular apex points in the zig-zag. These points are read out of the triangular network by the vertical alignment of the triangular apex points (vertical dashed red arrow) projected down onto the horizontal frequency difference scale. This yields an estimate for the average frequency spacing of the nulls (Δf = 10 kHz). The corresponding reciprocal of 100 μs is registered on the horizontal delay difference scale and the spacing of the glint reflections in the echo. (D) The 100-μs glint delay estimate from the triangular network in C (red arrow) is attached to the 6 ms overall echo delay estimate from the thresholds in B (blue arrow) to form an image of the target’s range and shape.