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. 2020 Jul 6;117(29):17288–17295. doi: 10.1073/pnas.2001105117

Fig. 1.

Fig. 1.

Role of FM harmonics in echo delay perception. (A) FM broadcast spectrogram has two down-sweeping harmonics (FM1: 55 to 25 kHz, FM2: 100 to 50 kHz). (B) Expected effects of low-pass (blue symbols and text) and high-pass (red symbols and text) filtering of echo spectra on delay acuity. Slight low-pass filtering of echoes by a small Δf = 4 kHz (narrow blue area at top of FM2 sweep) truncates the upper end of the echo spectrum by only that amount. Stronger low-pass filtering by larger Δf = 10 kHz (wider blue area) still only affects the upper end of FM2. In contrast, slight high-pass filtering by a small Δf = 4 kHz (narrow red area at lower end of FM1 sweep) also removes the corresponding second harmonic by 2Δf = 8 kHz from FM2 (vertical blue arrow projecting to wider red segment at lower end of FM2), for a total frequency loss of 3Δf = 12 kHz. More extensive high-pass filtering by a large Δf = 14 kHz (broad red segment of FM1 sweep) also removes 2Δf = 28 kHz from FM2 (wider red segment of FM2), for a total frequency loss of 3Δf = 42 kHz. (C) Removal of lower FM1 frequencies reduces delay acuity 3 times more than removal of the same bandwidth in upper FM2 frequencies (replotted from ref. 7). Thresholds for delay acuity by two big brown bats detecting small changes in delay (vertical axis; circles and diamonds) in a series of echoes with different high-pass and low-pass cutoff frequencies expressed as reductions in frequency content (horizontal axis, Δf in kHz). Removing frequencies from the top of FM2 (115 dB/octave cutoffs from 89 down to 55 kHz) increases delay change detection thresholds from 10 to 36 ns (blue data points and regression line); removing frequencies from the bottom of FM1 (115 dB/octave cutoffs from 15 up to 35 kHz) increases thresholds from 10 to 71 ns (red data points and regression line). From spectrograms in A, the slope of the high-pass results should be 3 times steeper than the slope of the low-pass results because removal of FM1 frequencies is magnified by removal of corresponding FM2 frequencies. The high-pass data also are rescaled vertically by 1/3 (green data points and regression line), which now parallels the low-pass results.