Spectrally specific temporal analyses of spike-train responses to complex sounds: A unifying framework
Fig 5
Envelope-coding metrics should be spectrally specific to avoid artifacts due to rectifier distortion and neural stochasticity.
Simulated responses for 24 AN fibers (log-spaced between 250 Hz and 8 kHz) were obtained using a computational model (parameters listed in S2 Table) using SAM tones at CF (modulation frequency, Fm = 20 Hz; 0-dB (100%) modulation depth) as stimuli. Stimulus intensity ∼ 65 dB SPL. S(f) (blue) and E(f) (red) for three example model fibers with CFs = 1.0, 1.7, and 4 kHz (panels A-C) illustrate the relative merits of s(t) and e(t), and the potential for rectifier distortion to corrupt envelope coding metrics. d(t) was band-limited to a 200-Hz band near Fc for each fiber prior to estimating e(t) from the Hilbert transform of d(t). (A) For the 1-kHz fiber, S(f) and E(f) are nearly identical in the Fm band. S(f) is substantially affected by rectifier distortion at 2 × CF, which can be ignored using spectrally specific analyses. (B) The two envelope spectra are largely similar near the Fm bands since phase-locking near the carrier (1.7 kHz) is still strong (panel D). Rectifier distortion in S(f) is greatly reduced since phase-locking at twice the carrier frequency (3.4 kHz) is weak. (C) Fm-related power in E(f) and rectifier distortion in S(f) are greatly reduced as the frequencies for the carrier and twice the carrier are both above the phase-locking roll-off. (D) The strength of modulation coding was evaluated as the sum of the power near the first three harmonics of Fm (gray boxes in panels A-C) for S(f) (blue squares) and E(f) (red circles). VSpp was also quantified to CF-tones for each fiber (black dashed line, right y-axis). (E) Rectifier distortion (RD) analysis was limited to the second harmonic of the carrier (brown boxes in panels A-C). RD was quantified as the sum of power in 10-Hz bands around twice the carrier frequency (2 × CF) and the adjacent sidebands (2 × CF ± Fm). RD for E(f) is not shown because E(f) was virtually free from RD. (F) Raw and adjusted sumcor peak-heights across CFs. sumcors were adjusted by band-pass filtering them in the three Fm-related bands. Large differences between the two metrics at low frequencies indicate that the raw sumcor peak-heights are confounded by rectifier distortion at these frequencies. (G) Relation between raw and adjusted sumcor peak-heights with Fm-related power (from panel D) in S(f). Good correspondence between Fm-related power in S(f) and adjusted sumcor peak-height supports the use of spectrally specific envelope analyses. (H) The difference between raw and adjusted sumcor peak-heights was largely accounted for by RD power. However, this difference was always greater than zero, suggesting broadband metrics can also be biased because of noise related to neural stochasticity.