Fig. 10.1
Auditory spectra for five complex tones with the same lowest component (15). The fundamental was 100 Hz and the tones had 2, 3, 5, 9 or 17 consecutive harmonics, all with the same level, 54 dB SPL
When there are only two primaries, there is only one component in the qDS and it is at 100 Hz, as expected. As NP doubles, the magnitude of the qDT at 100 Hz increases and the range of components in the qDS increases; that is, primaries that are farther apart in frequency contribute qDTs at higher difference frequencies. In the CAR-FAC system, the magnitude of the qDT increases with qDT frequency from 100 to 300 Hz; above this frequency, qDT magnitude decreases. In contrast, in the data of Pressnitzer and Patterson (2001), the qDT at 100 Hz has the greatest magnitude, and magnitude decreases monotonically as qDT frequency increases.
In this example, where the level of the primaries is fixed, the magnitude of the qDS grows with the number of primaries in absolute terms, and it grows even more with respect to the magnitude of the PS. This is because, locally, cochlear compression is driven by the overall level of the input. Thus, as NP increases and the PS broadens above 1,500 Hz, the response at 1,500 Hz decreases as the compression increases. Suppression grows within the PS as NP increases, and as a result, the PS develops edge tones when NC is 8 or more.
These initial simulations indicate that the compression applied by CAR-FAC systems produces distortion spectra that are similar in many respects to those observed by Pressnitzer and Patterson (2001), although the magnitudes of the qDTs in the CAR-FAC system do not decrease monotonically with increasing frequency as they do in the behavioural data.
Quadratic distortion products are known to have a pronounced effect on the lower limit of melodic pitch (Pressnitzer et al. 2001; Pressnitzer and Patterson 2001, 2001) and the detection of low-frequency tones in the presence of high-frequency bands of amplitude-modulated noise (Wiegrebe and Patterson 1999). Accordingly, we examined the degree to which Lyon’s (2011) CAR-FAC system could explain the DS produced by complex tones.
2 The Effects of Compressive Distortion in CAR-FAC Systems
The parameter values for the CAR-FAC system were those referred to as “fit 507” of the “pole-zero filter cascade” (Lyon 2011, Fig. 6, PZFC). This version of the system provides a good fit to a wide range of notched-noise masking data, and it produces pronounced quadratic distortion. The CAR-FAC system was used to generate sets of auditory spectra for a complex tone presented at levels varying from 40 to 80 dB SPL in 10 dB steps. The fundamental of the tone was 200 Hz and it had 11 adjacent harmonics. The lowest component, LC, of the tones was varied from 1 to 16 in doublings to survey the parameter space and locate typical distortion patterns. Broadly speaking, tones with LC equal 1, 2 or 4 produced similar patterns of AS, and high-frequency tones with LC equal 8 or 16 produced similar patterns of AS, so the results will be described for two tones: one with LC = 2 and the other with LC = 8.
2.1 Auditory Spectra for High-Frequency Complex Tones (LC 8)
Three sets of AS were generated for LC 8 (right-hand column of Fig. 10.2). The AS for the standard CAR-FAC system are shown in the middle-right panel. The PS show that the primaries are not resolved; the DS reveal resolved peaks at the first four harmonics of the fundamental. The sequence of PS shows that the system is compressive; in the range 40–60 dB SPL, each 10-dB step in stimulus level produces a roughly equal change in the level of the PS. As the level of the tone increases to 70 and then 80 dB SPL, the magnitude of the increase in the PS increases. Nevertheless, the system remains compressive; the increases in AS level are far less than an order of magnitude in both cases. Over the same range of levels (60–80 dB SPL), the magnitude of the DS increases at a slower rate than it does at lower levels. Moreover, the pattern of PS activity changes above 60 dB SPL: there is an increase in suppression in the central region of the PS, leading to more pronounced edge tones; there is an increase in the magnitude of the fourth harmonic of F0; and there is an increase in the response in the region between the PS and the qDS. These are the characteristics of cubic distortion as they appear in the AS of the CAR-FAC system.
Fig. 10.2
Auditory spectra for a 200-Hz complex tone with 11 harmonics at levels from 40 to 80 dB SPL in 10-dB steps; LC is 2 (left column) or 8 (right column). The middle row shows the AS produced with the CAR-FAC system. The lower row shows the AS when the cubic compressor is turned off; the upper row shows the AS when the cubic compressor is turned off and HWR is replaced with FWR/2
The cubic compressor in the CAR-FAC system reduces the amplitude of the output of each section, by a small proportion of the cube of what would otherwise be the output, before the output passes to the next stage. In the model, it is associated with the operation of the outer hair cell. The input/output function for the compressor is radially symmetric, so it would be expected to introduce cubic distortion tones (cDTs) of the form 2f 1–f 2 rather than qDTs of the form f 2–f 1 (where f 1 and f 2 are the frequencies of two primaries). For a complex tone, cubic distortion appears as a spectrum of harmonics cascading down in frequency and magnitude from the low-frequency side of the PS. It will be referred to as the cubic portion of the distortion spectrum (cDS), and this is what appears in the AS at the higher tone levels (70 and 80 dB SPL). For comparison, the bottom-right panel of Fig. 10.2 shows the set of AS generated when the cubic compressor is turned off (CC off). The cDS that appears in the middle-right panel at 80 dB SPL disappears, and the suppression in the PS is greatly reduced, confirming that these are aspects of cubic compression. Note also that the qDS persists at low frequencies in the bottom-right panel when the cubic compressor is turned off. Indeed, the magnitude of the qDS increases at the higher tone levels (70 and 80 dB SPL) indicating that in this model, the cubic distortion suppresses the qDS at high stimulus levels.
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