Swinbanks, M.A. Enhanced Perception of Infrasound….
Low Frequency 2012
15th Conference on Low Frequency Noise
Stratford-upon-Avon, UK, May 2012
Enhanced Perception of Infrasound in the Presence of Low-Level Uncorrelated Low-Frequency Noise.
In prior work, the author has presented a technique for evaluating perception of infrasound and low-frequency noise, relative to the threshold of hearing, by a cumulative integration process which matches the mean energy of the sound to that of an equivalent sinusoid at the hearing threshold.
The author demonstrated that this approach, while rigorous, fails to take account of the crest factor of the sound, which can be very much greater than that of a pure sinusoid. Time domain simulation of the hearing response to real signals near the hearing threshold showed that taking the effect of crest factor into account, low frequency and infrasound may be perceptible at significantly lower levels than those defined by the simple criterion of equating mean sound energy.
This analysis has now been developed further, using time-domain simulation to take account of a well-defined hearing threshold, together with the effects of additional, uncorrelated low-frequency noise present within the same critical bandwidth (1Hz – 100Hz). The results of dynamic simulation show that in the presence of such uncorrelated, low-level noise, unwanted low-frequency sound and infrasound may be perceived at levels which would otherwise be completely dismissed as being well below the threshold of hearing.
These conclusions will be shown to be consistent with prior reported peer-reviewed laboratory experimental data, which hitherto has defied immediate explanation.
In a prior paper  the author proposed methods of assessing the audibility of low-frequency and infrasonic noise, enabling the characteristics of broad-band or impulsive noise to be assessed with respect to the threshold of hearing. A brief review of these procedures will first be given, since the specific techniques form a basis for the more extended methodology which will be described in the present paper.
This overall investigation started from the observation by T.H.Pedersen  that direct comparison of spectral levels of sound with the hearing threshold cannot be used to define the transition to audibility, since different resolution bandwidths give rise to different apparent spectral levels.
(See Figure 1 on downloadable document below)
This problem arises because such a comparison involves two entirely different physical measures. The threshold of hearing is determined by testing with single isolated sinusoidal tones to determine at what level the tone first becomes audible. In comparison, any measure of spectral sound level represents an assessment of multiple, complex components presented simultaneously to the ear.
Tonal measurement of the ear’s hearing threshold effectively measures the inverse of the frequency-response (transfer function) of the ear at the threshold level, so Pedersen proposed that the different spectral levels should first be weighted with the inverse hearing threshold, to represent the spectrum of the sound after having passed through this transfer function. Under this transformation, the threshold of hearing now becomes a constant level at 0dB, for all frequencies, but it can be seen that different spectral resolutions still give rise to different levels relative to this uniform threshold. (Figure 2)
(See Figure 2 on downloadable document)
Pedersen therefore recommended that the spectra should be integrated over the two lowest critical bands of hearing, 1-100Hz and 100Hz to 200Hz, resulting in two values common to all spectra, which would determine whether the sound exceeded the threshold in these two respective bands.
This procedure does not, however, indicate at what specific frequency the sound first becomes audible, since the lowest critical band simultaneously encompasses infrasonic frequencies, extremely low audible frequencies, and moderately low frequencies. The present author therefore proposed that this shortcoming could be addressed by performing instead a running integration of the spectral levels. This process results in all the spectra of differing resolution being condensed to a single, common line. (Figure 3). The frequency at which this cumulative spectrum intersects the 0dB axis represents the frequency at which the spectrum first contains sufficient energy to match the equivalent energy of a single, just-audible, pure tone.
(See Figure 3 on downloadable document)
Such an assessment equates the rms sound pressure, or mean sound energy, with that of a pure sinusoidal tone at the hearing threshold. In practice, the crest factor of real acoustic signals, particularly impulsive signals, can be much higher than the crest factor of a pure tone, and consequently may reach the threshold and become audible at lower rms levels. To investigate this, the present author proposed simulating the transfer function of the ear as a time-domain digital filter (Figure 4), and passing the time histories of the relevant sound through this filter to establish the actual levels relative to the (now constant-amplitude) hearing threshold.
(See Figures 4 and 5 on downloadable document)
Figure 5 shows four examples of simulated periodic, impulsive infrasonic noise passed through this filter. Three different levels of random background noise were mixed with these impulses, to assess the effects of differing signal-to-noise ratios.
The corresponding cumulative spectra defining the temporal levels at which the resultant outputs clearly met the threshold limits are shown in Figure 6. Dependent on the precise signal-to-noise ratio, it can be seen that the sound would be considered to meet the limits and become perceptible at significantly lower rms levels than the 0dB level.
(See Figure 6 on downloadable document)
This result is essentially consistent with actual acoustic test results carried out by NASA in 1982 to establish the levels of audibility of impulsive low-frequency noise generated by the then noisier, downwind turbines. 
These results have been obtained by comparison of time-histories, or cumulative frequency-spectra with the hearing threshold, after appropriate compensation for the transfer function of the ear at the hearing threshold. Such processes represent entirely linear operations, so that there is no cross-coupling of frequency components.
In the present paper, the effect of passing the filtered time-histories through a finite threshold operation will be considered. This process introduces interaction between low-frequencies and high-frequencies within the same critical bandwidth, and it will be shown that this can make a significant impact on the assessment of perception or audibility.