**3. Loudness and annoyance in relation to the effective duration of the ACF,** *τe*

#### **3.1. Loudness in relation to IRN**

Previous investigations of the relationship between loudness and the BPN bandwidth have concluded that for sounds with the same SPL, loudness remains constant as bandwidth increases, up until the point at which the bandwidth reaches a critical band. For bandwidths larger than the critical band, loudness increases with bandwidth [25]. However, the loudness of a sharply filtered BPN increases with the effective duration of the ACF, i.e., *τe*, even when the bandwidth of the BPN is within the critical band [26]. The *τe* value represents the repetitive components within the signal itself and increases as the BPN bandwidth decreases. However, the envelope and SPL also vary with the BPN bandwidth. This variation of the envelope and SPL might therefore affect the loudness of a BPN signal [27, 28]. To eliminate the effects of these factors, we investigated the effects of *τe* on loudness using IRN. The envelope and SPL variation of the IRN are much smaller than those of the BPN [29].

We produced IRN by applying a delay-and-add algorithm to the BPN that was filtered from white noise using the fourth-order Butterworth filters ranging between 100 and 3500 Hz. The number of iterations of the delay-and-add process was set at 2, 4, 8, 16, and 32. The delay values were set at 0.5, 1, 2, 4, 8, and 16 ms, corresponding to pitches of 2000, 1000, 500, 250, 125, and 62.5 Hz, respectively. The duration of the stimuli was 0.5 s and the rise and fall ramps were 10 ms. The sounds were D/A converted with a 16-bit sound card and sampling rate of 48 kHz. The sounds were presented at a SPL of 60 dB through insert earphones inserted into the left and right ear canals. **Figure 13** shows the *τe* and *φ*1 values of the IRN used in the experiment.

Psychophysiological Evidence of an Autocorrelation Mechanism in the Human Auditory System http://dx.doi.org/10.5772/66198 199

**Figure 12** shows the relationship between *φ*1 of the BPN and the N1m amplitude. A larger *φ*<sup>1</sup> produced a larger N1m response. The correlation coefficient was 0.65 (*p* < 0.05). However, we identified another factor that influences N1m amplitude. To calculate the effects of each ACF factor on AEF response, we conducted multiple regression analyses with the N1m amplitude as the outcome variable. We used a linear combination of *φ*1, *τ*1, and *τ*e as predictive variables in a stepwise fashion. The final version indicated that *φ*1 and *τ*e were significant factors:

> N1m amplitude \* \* »++ *aab* 31 4e 2 f

ACF factors *φ*1 and *τe* had significant effects on N1m responses.

of the IRN are much smaller than those of the BPN [29].

*τe*

**3.1. Loudness in relation to IRN**

198 Advances in Clinical Audiology

in the experiment.

The model was statistically significant (*p* < 0.01), and the correlation coefficient between the measured and predicted values was 0.78. The standardized partial regression coefficients of the variables *a*3 and *a*<sup>4</sup> in Eq. (4) were 0.52 and 0.45, respectively. The results indicated that the

**3. Loudness and annoyance in relation to the effective duration of the ACF,**

Previous investigations of the relationship between loudness and the BPN bandwidth have concluded that for sounds with the same SPL, loudness remains constant as bandwidth increases, up until the point at which the bandwidth reaches a critical band. For bandwidths larger than the critical band, loudness increases with bandwidth [25]. However, the loudness of a sharply filtered BPN increases with the effective duration of the ACF, i.e., *τe*, even when the bandwidth of the BPN is within the critical band [26]. The *τe* value represents the repetitive components within the signal itself and increases as the BPN bandwidth decreases. However, the envelope and SPL also vary with the BPN bandwidth. This variation of the envelope and SPL might therefore affect the loudness of a BPN signal [27, 28]. To eliminate the effects of these factors, we investigated the effects of *τe* on loudness using IRN. The envelope and SPL variation

We produced IRN by applying a delay-and-add algorithm to the BPN that was filtered from white noise using the fourth-order Butterworth filters ranging between 100 and 3500 Hz. The number of iterations of the delay-and-add process was set at 2, 4, 8, 16, and 32. The delay values were set at 0.5, 1, 2, 4, 8, and 16 ms, corresponding to pitches of 2000, 1000, 500, 250, 125, and 62.5 Hz, respectively. The duration of the stimuli was 0.5 s and the rise and fall ramps were 10 ms. The sounds were D/A converted with a 16-bit sound card and sampling rate of 48 kHz. The sounds were presented at a SPL of 60 dB through insert earphones inserted into the left and right ear canals. **Figure 13** shows the *τe* and *φ*1 values of the IRN used

 t

(4)

**Figure 13.** (a) *τe* and (b) *φ*1 of the IRN used in the experiment as a function of the number of iterations with delays of (○) 0.5, (△) 1, (□) 2, (●) 4, (▲) 8 and (■) 16 ms.

Ten listeners (aged 21−37 years) with normal hearing took part in the experiment. We obtained loudness matches using a two-interval, adaptive forced-choice procedure converging on the point of subjective equality (PSE) following a simple 1-up, 1-down rule [30]. The experiment took place in a soundproof room. In each trial, the fixed (test) and variable (reference) sounds were presented in randomized order with equal probability at an interval of 500 ms. The test sound was an IRN and the reference sound was a 1-kHz pure tone. The listener was asked to indicate which sound they perceived as louder by pressing a key on a keyboard. For each

**Figure 14.** Mean PSE for loudness (± standard error) across 10 listeners as a function of (a) *τe* and (b) *φ*<sup>1</sup> for IRN with a delay of (△) 0.5, (□) 1, (○) 2, (●) 4, (▲) 8 and (■) 16 ms.

adaptive track, the overall level of the test sound was fixed at 60 dB SPL, and the starting level of the reference sound was 50 dB SPL. The level of the reference sound was controlled with an adaptive procedure: when the listener judged the reference sound to be louder than the test sound, the SPL of the test sound was lowered by a given amount, and when the listener judged the test sound to be louder than the reference sound, the SPL of the reference sound was increased by that same amount.

**Figure 14** shows the PSE for loudness as a function of *τe* and *φ*1 of the IRN. *φ*<sup>1</sup> was not correlated with the perceived loudness. When *τe* was between 10 and 100 ms, the perceived loudness increased with *τe*, clearly confirming that loudness is influenced by the repetitive components of sounds [26] in the *τe* range between 10 and 100 ms. The increase in loudness for the *τe* values between 10 and 100 ms was approximately 5 dB.

When *τe* was less than 5 ms, the loudness of the IRN increased with decreasing *τe* and the bandwidth of the IRN was larger than the critical bandwidth. These tendencies may explain the basis of the critical band effect, such that loudness remains constant as the bandwidth of the noise is narrower than the critical band, then increases with increasing bandwidth beyond the critical band [25]. Loudness models are able to predict these tendencies [31, 32].

The loudness model introduced previously [31, 32] was unable to predict loudness when the delays were 2 and 4 ms for stimuli with a pitch of 500 and 250 Hz, respectively. Loudness increases caused by a tonal component are predictable according to *τe* in a certain range. Previous studies have indicated that the *τe* values of various noise sources, such as airplanes [33], trains [34], motor bikes [35] and flushing toilets [36], are within the range of 1–200 ms. This suggests that *τe* is a useful criteria for measuring the loudness of various sounds. Thus, this value is likely helpful for the identification of sound sources.

#### **3.2. Annoyance in relation to BPN**

Annoyance is one of the most commonly studied features of environmental noise [37]. Basically, psychoacoustic annoyance depends on loudness and other factors such as timbre and the temporal structure of sounds. Loudness and annoyance have been distinguished previously: Annoyance is the reaction of an individual to noise within the context of a given situation, while loudness is directly related to SPL [38]. To evaluate whether annoyance is related to the effective duration of the ACF, i.e., *τe*, we examined the annoyance elicited by a pure tone and BPN stimuli with different bandwidths.

We used pure tone and BPN signals with center frequencies of 1000 and 2000 Hz as auditory signals. We used a maximum length bandpass filtered sequence signal (order 21; sampling frequency, 44,100 Hz) as the basic stimulus. To control the ACF of the BPN, we varied the filter bandwidth at 0, 40, 80, 160, and 320 Hz using a cut‐off slope of 2068 dB/octave. The sounds were D/A converted with a 16‐bit sound card and sampling rate of 48 kHz. The sounds were presented to both the left and right ears at an SPL of 74 dBA using headphones (Sennheiser HD‐340). **Figure 15** shows *τe* of the stimuli used in the experiment.

Psychophysiological Evidence of an Autocorrelation Mechanism in the Human Auditory System http://dx.doi.org/10.5772/66198 201

adaptive track, the overall level of the test sound was fixed at 60 dB SPL, and the starting level of the reference sound was 50 dB SPL. The level of the reference sound was controlled with an adaptive procedure: when the listener judged the reference sound to be louder than the test sound, the SPL of the test sound was lowered by a given amount, and when the listener judged the test sound to be louder than the reference sound, the SPL of the reference sound was

**Figure 14** shows the PSE for loudness as a function of *τe* and *φ*1 of the IRN. *φ*<sup>1</sup> was not correlated with the perceived loudness. When *τe* was between 10 and 100 ms, the perceived loudness increased with *τe*, clearly confirming that loudness is influenced by the repetitive components of sounds [26] in the *τe* range between 10 and 100 ms. The increase in loudness for the *τe* values

When *τe* was less than 5 ms, the loudness of the IRN increased with decreasing *τe* and the bandwidth of the IRN was larger than the critical bandwidth. These tendencies may explain the basis of the critical band effect, such that loudness remains constant as the bandwidth of the noise is narrower than the critical band, then increases with increasing bandwidth beyond

The loudness model introduced previously [31, 32] was unable to predict loudness when the delays were 2 and 4 ms for stimuli with a pitch of 500 and 250 Hz, respectively. Loudness increases caused by a tonal component are predictable according to *τe* in a certain range. Previous studies have indicated that the *τe* values of various noise sources, such as airplanes [33], trains [34], motor bikes [35] and flushing toilets [36], are within the range of 1–200 ms. This suggests that *τe* is a useful criteria for measuring the loudness of various sounds. Thus,

Annoyance is one of the most commonly studied features of environmental noise [37]. Basically, psychoacoustic annoyance depends on loudness and other factors such as timbre and the temporal structure of sounds. Loudness and annoyance have been distinguished previously: Annoyance is the reaction of an individual to noise within the context of a given situation, while loudness is directly related to SPL [38]. To evaluate whether annoyance is related to the effective duration of the ACF, i.e., *τe*, we examined the annoyance elicited by a

We used pure tone and BPN signals with center frequencies of 1000 and 2000 Hz as auditory signals. We used a maximum length bandpass filtered sequence signal (order 21; sampling frequency, 44,100 Hz) as the basic stimulus. To control the ACF of the BPN, we varied the filter bandwidth at 0, 40, 80, 160, and 320 Hz using a cut‐off slope of 2068 dB/octave. The sounds were D/A converted with a 16‐bit sound card and sampling rate of 48 kHz. The sounds were presented to both the left and right ears at an SPL of 74 dBA using headphones (Sennheiser

the critical band [25]. Loudness models are able to predict these tendencies [31, 32].

this value is likely helpful for the identification of sound sources.

pure tone and BPN stimuli with different bandwidths.

HD‐340). **Figure 15** shows *τe* of the stimuli used in the experiment.

increased by that same amount.

200 Advances in Clinical Audiology

**3.2. Annoyance in relation to BPN**

between 10 and 100 ms was approximately 5 dB.

**Figure 15.** The measured effective duration of NACF, i.e., *τe*, of the signal as a function of the bandwidth. Different symbols indicate different frequencies: (◯): 1000 Hz; (△): 2000 Hz.

Eight listeners aged 21−23 years with normal hearing took part in the experiment. We performed paired-comparison tests for all combinations of the pairs of the pure tone and BPN stimuli. The duration of the stimuli was 2.0 s, the rise and fall times were 50 ms, the silent interval between the stimuli was 1.0 s, and the interval between the pairs was 3.0 s, which was the time during which the listeners were expected to make a response. They were asked to judge which of the two sound signals was more annoying. We calculated the scale values of the annoyance rated by each listener according to Case V of Thurstone's theory [39].

The relationship between the scale values of annoyance and *τe* is shown in **Figure 16**. The averaged scale values of annoyance increased as *τe* increased within the critical band for both center frequencies of 1000 and 2000 Hz. The *τe* value represents the repetitive feature or tonal component of the auditory signals. Previous research suggests that tonal components increase the perceived annoyance and noisiness of broadband noise [35, 40, 41]. This is consistent with the present results. Two of the eight listeners reported the least annoyance for pure tone stimuli, with BPN stimuli with the widest bandwidth and a center frequency of 2000 Hz rated as the most annoying. In other words, annoyance increased as *τe* decreased. This could indicate that the effects of *τe* on annoyance are subject to individual variation.

**Figure 16.** Scale value of annoyance as a function of *τe* for BPN with a center frequency of (a) 1000 Hz and (b) 2000 Hz. Each symbol represents one listener. The line represents the mean scale value of the eight listeners.

## **4. Concluding remarks**

In this study, we investigate the effects of ACF factors on physiological and psychological responses. As a result, we found that the ACF factors *φ*1, *τ*1, and *τe* had significant effects on N1m response, suggesting that ACF factors are used as cues in the auditory cortex. We also found that the ACF factors *φ*1 and *τe* influence loudness and annoyance, suggesting that ACF factors are used as a cue for perception. These results indicate that the human auditory system has an autocorrelation-like mechanism.

### **Acknowledgements**

This work was supported by Grants-in-Aid for Scientific Research (B) (Grant No. 15H02771) from the Japan Society for the Promotion of Science.

#### **Appendix**

Auditory evoked fields (AEFs): Magnetic fields evoked by any abrupt sound or change in a continuous sound in the auditory cortex.

Butterworth filters: A kind of signal processing filter widely used for bandpass filtering.

Bandpass filtered noise (BPN): A noise in which frequency components are limited by bandpass filtering.

Envelope: Approximate shape of a sound wave form calculated by joining the peak amplitude.

Equivalent current dipole: A dipole estimated from the measured magnetic fields in the human brain, widely used in MEG analysis.

Interspike interval: Observed time between spikes from a single neuron.

Magnetoencephalography (MEG): A noninvasive technique for investigating human brain activity by measuring the magnetic fields produced by electric currents flowing in neurons.

Multiple regression analysis: A statistical technique for predicting a dependent variable from independent variables.

Paired-comparison tests: A psychophysical method that measures a linear distance among paired stimuli.

Point of subjective equality (PSE): Any of the points along a stimulus dimension at which a variable stimulus is judged by a listener to be equal to a standard stimulus.

Pure tone: A tone with a frequency component and a sinusoidal wave.

Tonotopic organization: Spatial arrangements in which sounds of different frequencies are processed in the auditory system.

Two-interval, adaptive forced-choice procedure: A psychophysical experimental design in which listeners are instructed to make a response between two alternatives within a timed interval, and the next alternative is determined by the previous response.

White noise: A random signal with equal intensity at all frequencies.
