Glossary of Symbols

n = 1, 2, 3. . . (2.15)

f 10-15; other examples of the unit: m, 10-3; μ, 10-6; n, 10-9; p, 10-12

f Frequency (Hz)

Flu_IACC Fluctuation of the IACC, which influences annoyance of noise (11.2)

Flu_τIACC Fluctuation of the τIACC, which influences annoyance of noise (11.4)

fl,r(t) Sound pressures arriving at the left and right ear entrances (2.12), (2.14)

F0 Fundamental frequency, the repetition period of a periodic sound.

F0a, f0b Fundamental frequencies of sounds A and B, (Fig. 6.3)

f Function of any one-dimensional subjective response in relation to physical factors (3.5), (6.1)

gl,r(t) Head-related impulse responses from a point source to two ear entrances in a room (2.13)

f(xi) Scale value as a function of the four orthogonal factors xi, i = 1, 2, 3, 4 (3.6)

h(t) Vertical and horizontal movements of the target (14.2)

hnl,r(t) Head-related impulse response from a point source to the leftand right-ear entrance of the n-th reflection (2.13)

IACC Magnitude of interaural crosscorrelation, which is the maximumm value of the interaural crosscorrelation function (IACF), the spatial factor of the sound field defined by (2.26). One of four orthogonal factors of the sound field.

i Alternative period of the mental tasks (i = 2n) (11.6)

Leq Equivalent sound-pressure level (SPL) measured after obtaining the signal envelope (2.8)

l(t) Luminance as a function of time of the stimulus produced by the LED (15.1)

LHorizontal Localization in the horizontal plane (7.1)

LMedian Localization in the median plane (7.2)

LL The binaural listening level (2.24). When the A-weighting network as an approximation of the ear sensitivity is used, the unit is given by dBA. One of the four orthogonal factors of the sound field.

O1, O2 see T3, T4

P The normalized ABR magnitude corresponding to the IACC (4.1)

P(ω) Pressure spectrum obtained by the Fourier transform of p(t) (2.2)

Pd(ω) Power density spectrum (2.1), (2.6)

p’l,r(t) p’l,r(t) = p(t) s(t), where pl.r(t) are the sound pressures arriving at left and right ear entrances, and s(t) is the ear sensitivity (2.4)

r12 Correlation coefficient between a sensation S1 and another sensation S2 defined by (6.4)

s Integer

s(t) Ear sensitivity expressed in the time domain (2.4). For the practical application, we can use the impulse response of the A-weighting filter as an approximation.

S Scale value of any subjective response (3.5); or the scale value of subjective preference of the sound field (3.7)

S Total surface in a room to determine the reverberation time (2.20)

Si Scale values of preference as a function of the listening level (LL), the initial time delay gap between the direct sound and the first reflection ( t1), the subsequent reverberation time (Tsub) and the IACC, respectively, i = 1, 2, 3, 4 (3.6), (3.7)

Sj Any primary sensation, j = 1, 2, ... J < I (6.1), (6.2)

SL, SR Temporal and spatial sensations, which are associated with the left and the right hemispheres, respectively (6.5). Overall subjective responses such as preference or annoyance are given by S = SL + SR (6.6).

SIK Speech intelligibility of the syllable K (%) (9.3)

s(t) Impulse response of the A-weighting filter, used as an approximation of ear sensitivity (2.22), so that f’l,r(t) = fl,r(t) s(t)

T Time interval (s) (2.4), (2.22)

T Tesla: unit of a magnetic flux density, 1T = 1Wb/m2

(2T)r Recommended temporal duration of signal segments to be used in running autocorrelation analyses, which is related to (τe)min (5.3)

T3, T4 Scalp locations for electrode placement according to the 10–20 International System. Temporal scalp locations (T3, T4, T5, T6) mainly reflect activity in auditory cortical regions of either the left (T3, T5) or right (T4, T6) hemisphere. Occipital locations (O1, O2) mainly reflect activity in visual cortical regions, Fig. 15.4., p. 269

326 Glossary of Symbols

Tsub Subsequent reverberation time defined by the decay rate to decrease to 60 dB

Vl,r(x,ω) Wave form of the basilar membranes, where x is the position measured along the left and right basilar membranes from the oval window, Fig. 5.1

WIACC Width of the IACC or width of the IACF at τIACC (7.3). One of the significant spatial factors related to apparent source width ASW (7.4–7.6), Fig. 2.8

wn(t) Impulse response describing the reflection property of a wall in a room, n = l, 2, 3,. . . (2.13), (2.18)

xi The normalized orthogonal factors, i = 1, 2, 3, 4 (3.6) through (3.11)

αAlpha wave (8-13 Hz) in EEG and MEG; the value of τe extracted from its ACF corresponds well with the scale value of subjective preference

α(t) Alpha wave as a function of time

αi Weights of the scale value of subjective preference for each orthogonal factor, i = 1, 2, 3, 4 (3.7), Table 3.4

α,β,γ Weighting coefficients of the spatial factor extracted from the IACF to calculate the scale value of ASW (7.6)

β All of results of the scale value of subjective preference as a function of a normalized factor obtained by the PCT are expressed commonly by the (3/2) power of the factor, such that , where α is the weighting coefficient.

(3.7): for normalized four orthogonal factors of the sound field of listeners;

(8.2): for the normalized factor of the sound field x = log t1 – log[ t1]p of cellists;

(14.1): for the normalized factor x = logφ1 – log[φ1]p of the visual field of observers;

(15.2): for the normalized period x = log10T – log10[T]p of the flickering light of observers;

(7.7): for describing the scale value of subjective diffuseness as a function of the IACC of listeners; and also,

[ tl]p Calculated preferred initial time delay gap between the direct sound and the first reflection (s), one of the temporal factors of the sound field (3.2), (3.4)

δ(t) Dirac delta function (2.13)

domain, defined by the delay time at which the envelope of the normalized ACF becomes and then remains smaller than 0.l (m)

( x, y) The two-dimensional ACF for describing spatial sensations of texture (13.1)

lr(ν) Auditory mechanism of the interaural crosscorrelation function (IACF), Fig. 5.1

lr(τ) Interaural crosscorrelation function (IACF) (2.22), (5.4)

p(τ) The autocorrelation function (ACF) of the signal p(t) (2.4), (2.5)

p(τ;τ,T) The short-time moving ACF or the running ACF (2.10)

p(0) Sound energy given by the time origin of p(τ), τ = 0 (2.7), (2.9)

ll(0), rr(0) ACF at the time origin, which corresponds to the sound energy at the left and right ear entrances, respectively (2.23), (2.24)

ll(σ), rr(σ) ACF mechanisms in the left and right auditory pathway, respectively, Fig. 5.1

ll(τ), rr(τ) ACF of the sound signals at the leftand the right-ear entrances, respectively (5.1)

the right ear (2.23), (2.24)

φ( x, y) Two-dimensional normalized ACF for describing spatial sensations of texture (13.2)

φ1 Amplitude at the first major peak at the delay τ1 in ACF, φp(τ), corresponding to perceived pitch strength, Fig. 2.1, or signal regularity, a degree of fluctuation of the signal

φlr(τ) Normalized interaural crosscorrelation function (2.23), (5.5)

φp(τ) Normalized ACF, φp(0) = 1 (2.7), (2.10)

η Elevation angle

ν Time delay (s)

σTime delay (s)

σStandard deviation

Summation

τ Time delay (s)

the normalized ACF becomes and then remains smaller than 0.l (the tenth-percentile delay) (s), Fig. 2.2. Effective duration is a measure of the temporal coherence of the signal, i.e. how long a stable temporal pattern faithfully repeats itself.

τIACC Interaural delay time, at which the maximum IACF (IACC) is observed, Fig. 2.8

τe(IACC = 0.3) Value of ACF τe of the EEG alpha wave obtained by the stimulus with IACC = 0.3 corresponding to a large spatial subjective diffuseness

τe(IACC = 0.95) Value of ACF τe of the EEG alpha wave obtained by the stimulus with IACC = 0.95 corresponding to a narrow subjective diffuseness, Fig. 4.22. The ratio of the values of τe for the alpha wave changing the IACC, [τe (IACC = 0.3)/τe(IACC = 0.95)] in the right hemisphere is greater than that in the left hemisphere, Fig. 4.23.

(τe)min Minimum value of τe obtained by analyzing the running ACF on a segment of source signal 2T (s), which is the most active part of the signal. Thus, subjective preference may be critically judged at this particular part in the music signal. For example, echo may be easily perceived at this running part.

τp Most preferred delay time of the first reflection, τe = [ tl]p (3.3)

ω Angular frequency (= 2πf, f being frequency [Hz])

ξ Horizontal angle of sound incidence to a listener (o)

Signals from the left and right auditory pathway to be combined, Fig. 5.1