ISO/TS 20065:2022
(Main)Acoustics — Objective method for assessing the audibility of tones in noise — Engineering method
Acoustics — Objective method for assessing the audibility of tones in noise — Engineering method
This document describes a method for the objective determination of the audibility of tones in environmental noise. This document is intended to augment the usual method for evaluation on the basis of aural impression, in particular, in cases in which there is no agreement on the degree of the audibility of tones. The method described can be used if the frequency of the tone being evaluated is equal to, or greater than, 50 Hz. In other cases, if the tone frequency is below 50 Hz, or if other types of noise (such as screeching) are captured, then this method cannot replace subjective evaluation. NOTE The procedure has not been validated below 50 Hz. The method presented herein can be used in continuous measurement stations that work automatically.
Acoustique — Méthode objective d'évaluation de l'audibilité des tonalités dans le bruit — Méthode d'expertise
Le présent document décrit une méthode de détermination objective de l’audibilité des tonalités dans le bruit environnemental. Le présent document est destiné à améliorer la méthode habituelle d’évaluation sur la base de l’impression auditive, en particulier en cas d’absence d’accord sur le degré d’audibilité des tonalités. La méthode décrite peut être utilisée lorsque la fréquence de la tonalité évaluée est égale ou supérieure à 50 Hz. Dans les autres cas, si la fréquence de la tonalité est inférieure à 50 Hz ou si d’autres types de bruit (par exemple un crissement) sont captés, la présente méthode ne peut pas remplacer l’évaluation subjective. NOTE Le mode opératoire n’a pas été validé pour des fréquences inférieures à 50 Hz. La méthode présentée ici peut être utilisée sur les postes de mesure continu qui fonctionnent automatiquement.
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Standards Content (Sample)
TECHNICAL ISO/TS
SPECIFICATION 20065
First edition
2022-12
Acoustics — Objective method for
assessing the audibility of tones in
noise — Engineering method
Acoustique — Méthode objective d'évaluation de l'audibilité des
tonalités dans le bruit — Méthode d'expertise
Reference number
© ISO 2022
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ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Measurement procedure . 6
4.1 General . 6
4.2 Measurement instruments . 6
4.3 Merging the basic spectra . 6
5 Evaluation . 6
5.1 General information. 6
5.2 Width, Δf , of the critical band . 7
c
5.3 Determination of prominent tones . 8
5.3.1 General information . 8
5.3.2 Determination of the mean narrow-band level, L , of the masking noise in
S
the critical band . 8
5.3.3 Determination of the tone level L of a tone in a critical band . 9
T
5.3.4 Distinctness of a tone . 10
5.3.5 Determination of the critical band level, L , of the masking noise . 10
G
5.3.6 Masking index . 11
5.3.7 Determination of the audibility, ΔL . 11
5.3.8 Determination of the decisive audibility, ΔL , of a narrow-band spectrum . 11
j
5.3.9 Determination of the mean audibility, ΔL, of a number of spectra .13
6 Calculation of the uncertainty of the audibility, ΔL .13
7 Recommendations on the presentation of results .16
7.1 Measurement . 16
7.2 Acoustic environment . 16
7.3 Instruments for measurement, recording and evaluation . 16
7.4 Acoustic data . 16
Annex A (informative) Window effect and Picket fence effect .17
Annex B (informative) Resolving power of the human ear at frequencies below 1 000 Hz
and geometric position of the critical bands – corner frequencies .20
Annex C (informative) Masking, masking threshold, masking index .22
Annex D (informative) Iterative method for the determination of the audibility, ∆L .23
Annex E (informative) Example for the determination of audibility .27
Bibliography .33
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
This first edition of ISO/TS 20065 cancels and replaces ISO/PAS 20065:2016, which has been technically
revised.
The main changes are as follows:
— guidance on residual sound (5.3.1);
— a file containing a number of other example audio files and a guidance document can be downloaded
from https://standards.iso.org/iso/ts/20065/ed-1/en (from “Prominent tones in wind turbine noise
Round robin test IEC 61400-11, ISO/PAS 20065”);
— editorial changes for clarity, for easier implementation in software, and to meet the latest ISO
standards, including definitions, measures, formulae, aligned and streamlined terminology, and
additional background information.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
TECHNICAL SPECIFICATION ISO/TS 20065:2022(E)
Acoustics — Objective method for assessing the audibility
of tones in noise — Engineering method
1 Scope
This document describes a method for the objective determination of the audibility of tones in
environmental noise.
This document is intended to augment the usual method for evaluation on the basis of aural impression,
in particular, in cases in which there is no agreement on the degree of the audibility of tones. The
method described can be used if the frequency of the tone being evaluated is equal to, or greater than,
50 Hz. In other cases, if the tone frequency is below 50 Hz, or if other types of noise (such as screeching)
are captured, then this method cannot replace subjective evaluation.
NOTE The procedure has not been validated below 50 Hz.
The method presented herein can be used in continuous measurement stations that work automatically.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 1996-1, Acoustics — Description, measurement and assessment of environmental noise — Part 1: Basic
quantities and assessment procedures
IEC 61672-1, Electroacoustics — Sound level meters — Part 1: Specifications
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 1996-1 and the following
apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
NOTE Unless otherwise stated, the reference level for decibel (dB) values in these definitions is 20 µPa.
3.1
tone
sound characterized by a single-frequency component or narrow-band components
3.2
tone frequency
f
T
frequency of the spectral line (3.23) (or mid-band frequency of the narrow-band filter), to the level of
which the tone (3.1) contributes most strongly
Note 1 to entry: Tone frequency is expressed in hertz (Hz).
3.3
tone level
L
T
energy summation of the narrow-band level (3.22) with the tone frequency (3.2), f , and the lateral lines
T
about f , assignable to this tone
T
Note 1 to entry: Tone level is expressed in decibels (dB).
Note 2 to entry: If the critical band (3.5) for the frequency, f , under consideration contains a number of tones,
T
then the tone level, L , is the energy sum of these tones. This level, L , is then assigned to the frequency of the
T T
participating tone that has the maximal value of audibility (3.4), ΔL.
Note 3 to entry: The method for the determination of the tone level, L , of a tone in a critical band is described in
T
5.3.3.
3.4
audibility
ΔL
Audibility of tones is the arithmetic difference between the tone level (3.3), L , and the masking threshold
T
′
(3.15), L
T
Note 1 to entry: Audibility is expressed in decibels (dB).
Note 2 to entry: The method for the determination of the decisive audibility (3.24), ΔL , of a narrow-band spectrum
j
(3.12) is described in 5.3.8.
3.5
critical band
frequency band with a bandwidth (3.17), ∆f within which the auditory system integrates the sound
c
intensity in the formation of loudness and within which it integrates the sound intensity in the
formation of the masking threshold (3.15)
Note 1 to entry: Critical band is expressed in hertz (Hz).
Note 2 to entry: This characteristic of a critical band (see also References [3] and [4]) holds only for a restricted
sound level range. This dependence is neglected here.
3.6
mean narrow-band level of the critical band
L
S
energy mean value of all narrow-band levels (3.22) in a critical band (3.5), except for the spectral line for
the frequency, f , under consideration and all lines that exceed this mean value by more than 6 dB
T
Note 1 to entry: Mean narrow-band level of the critical band is expressed in decibels (dB).
Note 2 to entry: The iterative method for the determination of the mean narrow-band level, L , of the masking
S
noise is described in 5.3.2 and in Annex D.
3.7
critical band level
L
G
level of noise that is assigned to the critical band (3.5) that describes the masking characteristic of the
noise for one or more tones of the noise in this critical band
Note 1 to entry: Critical band level is expressed in decibels (dB).
Note 2 to entry: See narrow-band level (3.22) and Annex C for masking.
Note 3 to entry: For the definition formula for L , see Formula (12).
G
3.8
sampling frequency
f
S
number of samples taken per second
Note 1 to entry: Sampling frequency is expressed in hertz (Hz).
Note 2 to entry: The analogue data provided continuously are converted into samples through sampling at
discrete time intervals for digital processing.
Note 3 to entry: To ensure the reproducibility of a digitized signal, the Shannon theorem requires that the
sampling frequency, f , is at least 2 times the highest frequency of the signal components used for evaluation in
S
the time signal [ f ≥ 2 f , see also aliasing (3.9), antialiasing filter (3.10) and useable frequency (3.20)]. Discrete
S N
Fourier Transform (DFT) analysers thus need a sampling frequency that is at least 2,56 times the maximum
frequency to be analysed.
3.9
aliasing
reflection in the line spectrum (3.12) of frequency components from the range above the sampling
frequency (3.8) divided by two ( f /2) in the range below f /2
S S
Note 1 to entry: Antialiasing filters (3.10) are used to avoid errors through such reflections.
Note 2 to entry: Half the sampling frequency ( f /2) is also known as the Nyquist frequency.
S
3.10
antialiasing filter
low-pass filter
ideal filter that allows frequencies below half the sampling frequency (3.8) to pass through completely
(without influencing the signal), but completely block all higher frequencies
Note 1 to entry: To prevent aliasing (3.9), the noise under investigation shall be filtered using an antialiasing
filter before analogue-to-digital conversion.
Note 2 to entry: Real aliasing filters have a final damping (generally 120 dB/octave) within the blocking range, i.e.
signal components in this transition range are reflected (damped). For example, in the transformation of 2 048
(2 k) data points, 1 024 frequency lines are calculated and 800 lines shown. A component in the line number
1 248 is folded back into the line number 800. With a low-pass filter of 120 dB/octave the damping of these
components is approximately 75 dB.
Note 3 to entry: The usual commercial DFT analysers have an antialiasing filter, the limit frequency of which
can be switched automatically with the selectable sampling frequency. The reflection of simulated narrow-band
levels (3.22) is suppressed.
3.11
block length
N
block of sampling values that in discrete form represents a time-limited range of the time signal to be
analysed
Note 1 to entry: In contrast to frequency analysis with analogue and digital filters, the noise with the Fast Fourier
Transform is processed in data blocks. In general, these blocks embrace only a part of the noise recording. The
block length, N, expresses the number of data points processed at the same time. Regarding the Fast Fourier
Transform, the value of N generally has the integer of power of 2. It has a value, for example, of N = 2 = 1 024
data points.
3.12
line spectrum
narrow-band spectrum
frequency spectrum
plot of the sound pressure level (narrow-band level) (3.22) as a function of the frequency in frequency
bands of constant bandwidth (3.17) (line spacing, ∆f ) (3.13)
Note 1 to entry: A-weighting of the level is assumed in this document.
Note 2 to entry: DFT analysis delivers a line spectrum, in which each line represents the output of a filter, the
mid-frequency of which corresponds to the frequency of the spectral line (3.23).
3.13
line spacing
frequency resolution
distance, between adjacent spectral lines (3.23), where the line spacing in the DFT is given by
Δff= /N
S
where
f is the sampling frequency (3.8);
S
N is the block length (3.11).
Note 1 to entry: Line spacing is expressed in hertz (Hz).
Note 2 to entry: In this document, the line spacing is 1,9 Hz ≤ Δf ≤ 4,0 Hz.
3.14
time window
time data set of the signal segment (block length) (3.11) that is multiplied by a weighting function
(window function)
Note 1 to entry: In accordance with the definition of the Fourier integral, a prerequisite of the DFT analysis is
that the time data set is periodic. If this is not the case (as with stochastic signals), cut-off effects at the edges
of the time window will lead to distortion of the spectrum. These distortions are avoided through weighting
functions such as the Hanning function.
Note 2 to entry: For more information on window and weighting functions, see, for example, Reference [5] and
Annex A.
3.15
masking threshold
′
L
T
audibility (3.4) threshold for a specific sound in the presence of a masking sound (masker)
Note 1 to entry: Masking threshold is expressed in decibels (dB).
Note 2 to entry: See Annex C for more information on the audibility threshold and the masking noise.
3.16
masking index
a
v
′
arithmetic difference between the masking threshold (3.15), L , and the critical band level (3.7), L , of
T G
the masking noise
Note 1 to entry: Masking index is expressed in decibels (dB).
Note 2 to entry: For frequency-dependent masking index, a , masking and masking noise, see Annex C.
v
3.17
bandwidth
frequency bandwidth
frequency range of a number of adjacent spectral lines (3.23)
Note 1 to entry: Bandwidth is expressed in hertz (Hz).
Note 2 to entry: If the width of a frequency band is calculated for which its beginning or end does not correspond
to the boundary between two spectral lines, then only the spectral lines that lie in their full width within the
calculated frequency range are assigned to the frequency band.
3.18
distinctness
clarity ratio of the prominence of a tone based on a bandpass noise to the prominence of a sinusoidal
tone of the same tone frequency (3.2), f , and same tone level (3.3), L
T T
Note 1 to entry: Distinctness is expressed in percentage (%).
3.19
edge steepness
slope of the level difference between the maximum narrow-band level (3.22) of a tone, L , and the
Tmax
narrow-band levels of the first line below/above the tone to the corresponding frequency difference
Note 1 to entry: Edge steepness is expressed in decibels per hertz (dB/Hz).
3.20
useable frequency
f
N
upper limit frequency of the signal components used for evaluation
Note 1 to entry: Useable frequency is expressed in hertz (Hz).
3.21
investigation range
frequency range within which tones are investigated in the line spectrum (3.12)
Note 1 to entry: Investigation range is expressed in hertz (Hz).
3.22
narrow-band level
averaged level within a spectral line (3.23)
Note 1 to entry: Narrow-band level is expressed in decibels (dB).
3.23
spectral line
frequency band of bandwidth (3.17), ∆f (line spacing) (3.13), in a line spectrum (3.12)
Note 1 to entry: Spectral line is expressed in hertz (Hz).
3.24
decisive audibility
ΔL
j
maximum audibility (3.4), ∆L in the individual spectrum, j
Note 1 to entry: Decisive audibility is expressed in decibels (dB).
3.25
mean audibility
ΔL,
energy average of decisive audibility (3.24), ΔLj, calculated for each narrow-band averaged spectrum
Note 1 to entry: Mean audibility is expressed in decibels (dB).
4 Measurement procedure
4.1 General
The measurement procedure will depend on the aims. The requirements for the measurement and
assessment procedure in terms of the choice of measurement point, measurement time and duration of
measurement, extraneous noise, etc. shall be satisfied.
The variable for determination of audibility of prominent tones is the sound pressure, p(t). For frequency
analysis, the A-weighted equivalent continuous sound pressure level, L , as given in ISO 1996-1, shall
Aeq
be established for the respective spectral lines. If the spectrum is unweighted ("LIN" or "Z"), then it
shall be corrected to A-weighting in accordance with IEC 61672-1.
4.2 Measurement instruments
Sound level meters that meet, or exceed, the requirements of Class 1 in IEC 61672-1 shall be used. These
have a frequency weighting “A”/“LIN” or “A”/“Z” with a lower limit frequency equal to, or below, 20 Hz.
Additional instruments such as recording instruments (digital or magnetic tape) may also be used. The
measured values derived through recording instruments shall lie within the tolerance range given in
IEC 61672-1.
Analysis of frequency components in the measurement signals is performed using a frequency
analyser. The constant line spacing, Δf, shall lie in the range 1,9 Hz to 4 Hz (inclusive). The use of the
Hanning window is mandatory in this document. For further processing, it shall be ensured that the
digitalization of the sound pressure signal across the entire dynamic range used has a resolution of at
least 0,1 dB.
Before it is processed further, the analogue measurement signal shall be passed through a steep low-
pass filter (antialiasing filter) to avoid errors in frequency analysis. The sampling frequency (see 3.8)
shall be at least two times the maximum usable frequency present (see 3.20). The Hanning window is to
be used as time window to reduce lateral bands (see 3.14).
4.3 Merging the basic spectra
The spectra for the prominent tone assessment shall have an averaging time of approximately 3 s. Due
to the line spacing of 1,9 Hz to 4 Hz (see 4.2) and the typical frequency range, f, of a few kHz, the basic
spectra given by the frequency analyser will have an averaging time below 1 s. To get the averaging
time of approximately 3 s, a number of basic spectra shall be merged. This shall be done line by line
with Formula (1):
1 N
01,dL / B
ij,
L = 10 lgd10 B (1)
i ∑
j=1
N
where
th th
L is the level of the i spectral line for the j spectrum, in dB;
i,j
N is the number of merged spectra.
5 Evaluation
5.1 General information
The aim of evaluation is to establish the audibility, ΔL. The procedure is the same for stationary and
non-stationary noises. For tones that can only just be perceived, a quaver (eighth note) is to be adopted
as a base time that is adequate for hearing. However, comprehensive studies have shown that the lower
limit for use of the procedure is reached at averaging times of approximately 3 s. Lower averaging times
lead to unjustified values of audibility, ΔL (too high, but also too low). Signals that have very high level
and/or frequency dynamics that no longer correspond with a 3-second averaging can, therefore, not be
evaluated using this document. The following conditions shall be satisfied for the measurements.
— The extended uncertainty, U, of the audibility, ΔL, with a coverage probability of 90 % in a bilateral
confidence interval (see Clause 6) shall not exceed ±1,5 dB. This is generally the case with evaluation
of at least 12 time-staggered narrow-band averaged spectra. If there are less than 12 averaged
spectra then the uncertainty shall be taken into consideration as given in Clause 6.
— Where there are alternating operating states, all of the operating states shall be covered by the
averaging spectra used (see Annex E).
Tones in different critical bands are evaluated separately. To arrive at a decision on whether an
assessment has to be made, only the critical band with the most pronounced tone is considered (see
5.3.8).
If a number of tones are present within a critical band, then an energy summation of their tone levels,
L , is carried out to yield a tone level, L (see 5.3.8).
Ti T
An assessment is performed for a tone only if its distinctness (see 3.18) is at least 70 %. This means
a maximal bandwidth, Δf , dependent on the tone frequency [see Formula (9)] and necessitates edge
R
steepness (see 3.19) of at least 24 dB/octave.
The mean audibility, ΔL, which is the conclusive result of this method for the noise to be assessed, is
determined by averaging in energy terms the decisive audibility ΔL calculated for each narrow-band
j
averaged spectrum. In this averaging, the ΔL , the maximum audibility in each spectrum, is used
j
regardless of the frequency of the tone. Because the aim of this method is to estimate the annoyance
of a noise containing tones relative to a noise without tones, not the annoyance of a tone at a particular
frequency.
NOTE 1 For the distinctness of a tone, see 5.3.4.
NOTE 2 Harmonic multiples of a tone are evaluated, independently of that tone, similarly to all other
components of the line spectrum.
A sample program to determine audibility can be downloaded from https:// standards .iso .org/ iso/ ts/
20065/ ed -1/ en. This is based on ISO/PAS 20065. It is useful for validating proprietary analysis codes.
5.2 Width, Δf , of the critical band
c
The width, Δf , of the critical band about the tone frequency, f , is given by Formula (2):
c T
06, 9
f /Hz
T
Δ=f 25,H07z,++5010,,14 Hz (2)
c
Assuming a geometric position of the corner frequencies of the critical band (see Annex B), these corner
frequencies, f and f , are derived as follows:
1 2
ff=× f (3)
T 12
2 2
−Δf Δff+4
()
c cT
f = + (4)
2 2
ff=+Δf (5)
21 c
5.3 Determination of prominent tones
5.3.1 General information
The audibility of a tone is determined using the tone level, L , and the critical band level, L , of the
T G
masking noise in the critical band about the tone frequency, f . The frequency of all maxima of the line
T
spectrum is considered as the tone frequency.
The use of the Hanning window is recommended in Annex A. With window functions (except for
rectangular windows), the effective analysis bandwidth, Δf , is greater than the bandwidth, Δf, of an
e
ideal filter (see 3.13), i.e. the individual bands are thus superimposed. In the summation process, the
energy components are counted a number of times (see Annex A for more information).
In a frequency analyser, this influence of summation (number of lines >1) is taken into consideration
through a correction value; if the level addition is simulated by the analyser program, then this
correction value has to be considered in the computing program, both in the formation of the tone level
[see Formula (8)] and in the calculation of the masking noise [see Formula (12)].
The measurement is to be made where possible at such times that tones from sources of residual
sound are not present as these can impact the assessment of the source of specific sound under
investigation. Justification of the selection of the measurement time period is to be reported. Where
not possible, the influence of the sources of residual sound on the measurement is to be reported. When
unattended measurements are used, ancillary data such as audio recording or other methods of source
identification are recommended. It is recommended that tones that are suspected of being caused
by sources of residual sound are excluded from analysis. In addition, it is recommended to consider
limiting the frequency range over which tones are searched for.
5.3.2 Determination of the mean narrow-band level, L , of the masking noise in the critical
S
band
The mean narrow-band level of the critical band, L , [see Formula (6)] is derived in an iterative procedure
S
from the lines of the critical band about the line under investigation. The procedure commences with
the energy averaging of all lines of the critical band with the exception of the line under investigation
itself. In the subsequent steps, the levels of the lines of the critical band under consideration are no
longer taken into consideration in the averaging procedure if their level exceeds the energy mean value
determined beforehand by more than 6 dB. The iterative procedure is discontinued, if in an iteration
step, the new energy mean value is equal within a tolerance of ±0,005 dB to that of the previous iteration
step or if the number of lines contributing to the mean narrow-band level to the right or left of the line
under investigation falls below a value of 5. In this case, the energy mean value from the last iteration
step, at which the number of energy averaged levels on both sides of the line under investigation in each
case was still at least 5 is used to form the mean narrow-band level.
For determination of the mean narrow-band level, the entire critical band about the line under
investigation is used. Consequently, the range under investigation (see 3.21) is limited relative to the
useable frequency, f , such that the upper limit of the uppermost critical band being considered does not
N
exceed the useable frequency, f . A corresponding condition also applies in principle for the lower limit
N
of the lowest critical band considered. Since the use of this document is restricted to tone frequencies
greater than or equal to 50 Hz and the usual analysers generate line spectra starting at 0 Hz, it is not
generally necessary to take any special precautions.
The mean narrow-band level of the critical band, L , is given by Formula (6):
S
1 M Δf
01,dL / B
i
L = 10 lg 10 + 10 lg dB (6)
S ∑
i=1
M Δf
e
where
th
L is the narrow-band level of the i spectral line of the critical band under consideration, in
i
decibels (dB);
M is the number of spectral lines to be averaged in the critical band;
Δf is the line spacing, in hertz (Hz) (see 3.13);
Δf is the effective bandwidth in Hz; if a Hanning window is used then the effective bandwidth, Δf ,
e e
is 1,5 times the frequency resolution (line spacing), Δf (see Annex A).
If the line spectrum is unweighted ("LIN" or "Z"), then it shall be A-weighted in accordance within
IEC 61672-1.
NOTE 1 If the iteration is discontinued, because the remaining number of spectral lines to be averaged on one
or both sides falls below 5, then the audibility can be somewhat greater than the audibility calculated with this
mean narrow-band level.
NOTE 2 The iteration procedure is described in Annex D.
NOTE 3 Using a digital calculation program, the equal condition in the iteration procedure is typically given
by the resolution of the number format (high resolution should be used).
5.3.3 Determination of the tone level L of a tone in a critical band
T
The tone level, L , is determined from the individual levels of the spectral lines in the critical band about
T
f that contain energy to be assigned to the tone. In principle, a tone may only be present if the level of
T
the spectral line considered is at least 6 dB greater than the corresponding mean narrow-band level, L .
S
In general, a number of spectral lines have to be taken into consideration, since, for instance, because
of the Picket fence effect (see Annex A), or actual small frequency fluctuations during data capture, the
tone energy is represented through the levels of a number of spectral lines.
Adjacent spectral lines should be used for summation purposes if
— they differ from the narrow-band level at a frequency, f , by less than 10 dB, and
T
— they differ from the mean narrow-band level, L , of the masking noise within the critical band about
S
the tone by more than 6 dB.
In case K = 1:
LL= (7)
TT
In case K > 1:
K Δf
01,dL / B
i
L = 10lg 10 +10lg dB (8)
T (∑ )
i=1
Δf
e
where
th
L is the narrow-band level of the i spectral line of this critical band with tone energy, in
i
decibels (dB);
K is the number of spectral lines with tone energy;
Δf is the line spacing, in hertz (Hz) (see 3.13);
Δf is the effective bandwidth, in hertz (Hz) (see 5.3.2).
e
NOTE The individual levels of the spectral lines with tone energy [see Formula (8)] also contain energy
components of the masking noise. These can generally be neglected.
5.3.4 Distinctness of a tone
The distinctness of a tone depends on the bandwidth of the tone and its edge steepness; if the
corresponding criteria are not satisfied then the tone is not audible to individuals with normal hearing.
If a tone based on bandpass noise has a distinctness of 70 % relative to that of a sinusoidal tone then
the maximum permitted bandwidth, Δf , as a function of the tone frequency, f , is approximated (see
R T
Figure 1 in Reference [8]) by:
Δ=ff26,,01 00Hz+ ,001 (9)
()
RT
The bandwidth of a tone with a frequency, f , is derived from the number of spectral lines, K [see
T
Formula (8)], multiplied by the line spacing, Δf.
First criterion: The bandwidth of the tone shall not exceed the maximum permitted bandwidth given
by Formula (9).
Second criterion: The edge steepness shall be at least 24 dB/octave.
This yields the level differences between the maximum narrow-band level of the tone, L , and the
Tmax
narrow-band levels of the first spectral line below the tone L /above the tone L as follows:
u o
The lower level difference ΔL is given by Formula (10):
u
f LL−
T Tmax u
Δ=L ≥24dB (10)
u
2 ff−
Tu
where
f is the frequency of the first spectral line below the tone, in hertz (Hz);
u
f is the frequency of the maximum narrow-band level, in hertz (Hz).
T
The upper level difference, ΔL , is given by Formula (11):
o
LL−
Tmax o
Δ=Lf ≥24dB (11)
oT
ff−
oT
where
f is the frequency of the first spectral line above the tone, in hertz (Hz);
o
f is the frequency of the maximum narrow-band level, in hertz (Hz).
T
5.3.5 Determination of the critical band level, L , of the masking noise
G
The level L is given by Formula (12):
G
Δf
c
LL=+ 10lg dB (12)
GS
Δf
where
L is the mean narrow-band level of the critical band, see 5.3.2;
S
Δf is the width of the critical band about the tone frequency, f , in hertz (Hz) (see 5.2);
c T
Δf is the line spacing (frequency resolution), in hertz (Hz).
5.3.6 Masking index
The masking index, a , is given by Formula (13):
v
25,
f /Hz
a =−21−+lg dB (13)
v
where f is the frequency, in hertz (Hz).
NOTE For information on the masking index, a , see Annex C.
v
5.3.7 Determination of the audibility, ΔL
The audibility, ΔL, between the tone level, L , (see 5.3.3) and the level of the masking threshold (see
T
3.15) is given by Formula (14):
Δ=LL()−−La (14)
TG v
where
L is the tone level, in decibels (dB) (see 5.3.3);
T
L is the masking noise, in decibels (dB) (see 5.3.5);
G
a is the masking index, in decibels (dB) (see 5.3.6).
v
NOTE Formula (14) holds correspondingly if all the parameters of that formula are given.
5.3.8 Determination of the decisive audibility, ΔL , of a narrow-band spectrum
j
To determine the audibility, ΔL, of a noise a number of narrow-band spectra (see Annex D), staggered in
time, of the noise with the same line width and same number of lines are used. The measurement time
for such a spectrum should be approximately 3 s. The decisive audibility, ΔL , of an individual spectrum
j
is determined in the following four steps. For simplification purposes the run index j is not given.
Step 1
Each spectral line, i, is investigated in ascending sequence to establish whether it represents a potential
tone. A narrow-band level is a potential tone if the following conditions are satisfied:
LL>>andLL (15)
ii+−11ii
and
LL>+6dB (16)
iiS
NOTE 1 Mean narrow-band level, L , see 5.3.2.
Si
Step 2
The tone levels, L , (see 5.3.3) of all the potential tones (run index k across all potential tones) is
Tk
determined. The masking noises, L (see 5.3.5), and the masking index, a (see 5.3.6), are determined
Gk vk
for the tone levels at which the condition of distinctness of a tone (see 5.3.4) is satisfied. These
parameters are used to calculate the corresponding audibilities, ΔL [see 5.3.7, Formula (14)].
k
If ΔL > 0, then a tone is present.
k
Step 3
Critical bands with the width, Δf , are formed about each of these audible tones, L (run index m
cm Tm
across all audible tones) of frequency, f .
Tm
If a number of tones are present in a critical band, then their tone levels, L (run index n across all
Tm,n
tones in the critical band; H is the number) are summed in terms of energy.
H
01,dL / B
T,mn
L = 10lg 10 dB (17)
Tm )
(∑
n=1
where
H is the total number of all tones in the critical band;
L is the tone level with the run index m across all audible tones and the run index n across all
Tm,n
tones in the critical band, in decibels (dB).
It is possible for the energy of individual spectral lines to be assigned to a number of neighbouring tones
at the same time. Upon addition of the tone levels of neighbouring tones, the energy of these individual
spectral lines may not be summed more than once.
The tone frequency, f , is the frequency of the most pronounced tone, i.e. the tone with the greatest
Tm
audibility, ΔL .
m,n
The mean narrow-band level of the masking noise is that mean narrow-band level that was calculated in
the iterative procedure in 5.3.2 [see Formula (6)] from the lines about the tone with this tone frequency.
The level of the masking noise is the critical band level, L , calculated with this mean narrow-band
Gm,n
level in accordance with 5.3.5.
This tone level, L , is used to recalculate the decisive audibility, ΔL (see Step 2).
Tm k
If exactly 2 tones with tone frequencies, f and f , appear in one critical band, then they are evaluated
T1 T2
separately if both tone frequencies lie below 1 000 Hz and the frequency difference, f .
D
ff=− f (18)
DT12T
where f , f < 1 000 Hz.
T1 T2
Formula (18) exceeds the following value (see Annex B):
18,
f /Hz
T
12,lg
f =×21 10 Hz (19)
D
where
50 Hz < f < 1 000 Hz;
T
f is the frequency of the more pronounced tone (the tone with the greater audibility, ΔL ).
T k
NOTE 2 If precisely 2 tones are present in a critical band below 1 000 Hz, then the human ear can distinguish
differences less than half the critical bandwidth (see Reference [6] and Annex B).
Step 4
The audibility with the maximum value, ΔL , is the decisive audibility, ΔL , of the individual spectrum.
k j
5.3.9 Determination of the mean audibility, ΔL, of a number of spectra
As given in 5.3.8, the decisive audibility, ΔL , is calculated for each narrow-band averaged spectrum
j
(run index j, J is the number). These J audibilities, ΔL , are averaged in energy terms to yield a ΔL:
j
J
1 01,dΔL / B
j
Δ=L 10 lgd10 B (20)
∑
j=1
J
where
ΔL is the decisive audibility, in decibels (dB);
j
j is the run index;
J is the number of spectra.
The tone frequencies are the frequencies of the tones to which the audibilities are assigned. To ensure
a sufficient distance from the positive audibilities, ΔL , for all spectra in which no tone is found, the
j
following value is used for ΔL :
j
ΔL = −10 dB (21)
j
No tone frequencies are stated for this ΔL .
j
NOTE The audibilities, ΔL (and not the tone levels, L ), are averaged in energy terms since the tones in the
j Tj
individual spectra have different tone frequencies, and thus, different masking index, a [see Formula (13)] and
v
masking noises [see Formula (12)] have to be calculated.
6 Calculation of the uncertainty of the audibility, ΔL
The mean audibility, ΔL, between the tone level and the level of the masking threshold of a noise is
calculated using Formula (20) from the decisive audibilities, ΔL , of the individual narrow-band spectra
j
(see 5.3.8 and 5.3.9):
1 J 01,dΔL / B
j
Δ=L 10lg 10 dB (22)
∑
j=1
J
ΔL is calculated through the use of Formula (14) and Formula (12):
j
Δf
c
j
Δ=LL −−L 10lg dB−a (23)
jjTS,,jjv,
Δf
with the expressions of
K
01,/L dB Δf
ji;
L = 10 lg 10 + 10 lg dB (24)
Tj, (∑ )
i=1
Δf
e
1 M 01,/L dB Δf
ji;
L = 10 lg 10 + 10 lg dB (25)
Sj, ∑
i=1
M Δf
e
25,
f / Hz
j
a =−21−+lg dB (26)
vj,
502
NOTE All frequencies are expressed in hertz (Hz).
Δf
c
j
A normal distribution within the level zone is to be assumed for the term 10lg .
Δf
No uncertainty is assumed for the masking index, a
v.
The L values are derived through summation and the L values through averaging of intensities. It
T,j S,j
is therefore necessary to assume a normal distribution of these values within the intensity range. To
simplify the procedure, however, a normal distribution within the sound level range is assumed for
all summands. Since, for the consideration of uncertainty, it is of interest to know the probability of
determining audibility of a tone or tones that is too low, and for the upper limit of the confidence interval
the consideration in the level zone yields greater uncertainties than a corresponding consideration in
the intensity zone, the agreement can be regarded as a safe estimation.
A number of sound sources act on the emission point and may be regarded as incoherent. Their emitted
output levels are uncorrelated in their statistical behaviour. The uncertainty consideration of L and
T
L is based only on the uncertainty of the level of the spectral lines involved. The question as to which
S
spectral lines contribute to L /L is neglected in the consideration of uncertainty h
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