ISO/TS 13473-4:2008

TECHNICAL ISO/TS
SPECIFICATION 13473-4
First edition
2008-05-01
Characterization of pavement texture by
use of surface profiles —
Part 4:
Spectral analysis of surface profiles
Caractérisation de la texture d'un revêtement de chaussée à partir de
relevés de profils de la surface —
Partie 4: Analyse spectrale des profils de la surface

Reference number
©
ISO 2008
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ii © ISO 2008 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 2
4 Basic outline of methodologies of spatial frequency analysis. 6
5 Sampling of surface profiles . 8
5.1 Sampling of road sections. 8
5.2 Measurement of laboratory samples . 9
6 General principles and requirements . 9
6.1 Requirements concerning profilometers .9
6.2 Conversion of spatial frequencies to temporal frequencies. 9
6.3 Drop-outs. 11
6.4 Anti-aliasing filtering . 12
6.5 Digital sampling . 12
7 Spectral analysis in constant-percentage bandwidth bands (octave- or one-third-octave
bands) by analogue filtering (Method 1). 13
8 Spectral analysis in constant-percentage bandwidth bands (octave- or one-third-octave
bands) by digital filtering (Method 2). 15
9 Spectral analysis in narrow constant bandwidth bands by means of Discrete (Fast)
Fourier Transform methods (Method 3) . 15
9.1 Overview of methodology. 15
9.2 Slope and offset suppression . 16
9.3 Windowing. 16
9.4 Discrete Fourier Transform and Power Spectral Density. 18
9.5 Wavelength resolution . 19
10 Transformation of constant bandwidth spectral data to constant-percentage bandwidth
spectral data. 19
11 Uncertainty of analysis results. 21
12 Reporting of analysis results . 22
Annex A (normative) Uncertainty of spectral analysis results. 23
Annex B (informative) Aliasing .28
Annex C (informative) Estimation of the deviation in energy within a frequency band caused by
variations in speed . 30
Annex D (informative) Compensation for speed variations during processing of the measured
data. 31
Annex E (informative) Explanation of the relation between the wavelength resolution and the
spatial frequency resolution. 32
Annex F (informative) Spectral analysis and profile asymmetry. 33
Bibliography . 35

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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of document:
— an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
— an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
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.
ISO/TS 13473-4 was prepared by Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
ISO 13473 consists of the following parts, under the general title Characterization of pavement texture by use
of surface profiles:
⎯ Part 1: Determination of Mean Profile Depth
⎯ Part 2: Terminology and basic requirements related to pavement texture profile analysis
⎯ Part 3: Specification and classification of profilometers
⎯ Part 4: Spectral analysis of surface profiles [Technical Specification]
⎯ Part 5: Determination of megatexture
iv © ISO 2008 – All rights reserved

Introduction
Pavement texture is one of the basic road surface characteristics and as such is related to many functional
characteristics, such as noise emission from tyre-road interaction, friction between tyre and road, rolling
resistance and tyre wear.
Spectral analysis of measured surface profiles is frequently used as a method of pavement characterization.
However, recent practice has shown that the methodology of spectral analysis is not sufficiently well known in
the field of pavement measurements to assure reproducible results. Improvement of the reproducibility by
offering guidance in the form of a standardization document seems therefore advisable.
Although the principles of frequency analysis are used in various fields of signal processing, it seems that a
tailored elaboration of these principles for the application in the field of pavement texture measurements is
appropriate and will enhance the use of these methods and the quality of the results achieved.
This elaboration, in the form of an ISO Technical Specification, is intended to stimulate the international
exchange of knowledge and data concerning pavement characteristics.

TECHNICAL SPECIFICATION ISO/TS 13473-4:2008(E)

Characterization of pavement texture by use of surface
profiles —
Part 4:
Spectral analysis of surface profiles
1 Scope
This Technical Specification describes the methods that are available to perform a spectral analysis of
pavement surface profile signals. It specifies three possible methods for spatial frequency analysis (or texture
wavelength analysis) of two-dimensional surface profiles that describe the pavement roughness amplitude as
a function of the distance along a straight or curved trajectory over the pavement.
The result of the frequency analysis will be a spatial frequency (or texture wavelength) spectrum in constant-
percentage bandwidth bands of octave or one-third-octave bandwidth.
This Technical Specification offers three alternative methods to obtain these spectra:
1) analogue constant-percentage bandwidth filtering;
2) digital constant-percentage bandwidth filtering;
3) constant narrow bandwidth frequency analysis by means of Discrete Fourier Transform, followed by
a transformation of the narrow-band spectrum to an octave- or one-third-octave-band spectrum.
The objective of this Technical Specification is to standardize the spectral characterization of pavement
surface profiles. This objective is pursued by providing a detailed description of the analysis methods and
related requirements for those who are involved in pavement characterization, but are not familiar with general
principles of frequency analysis of random signals. These methods and requirements are generally applicable
to all types of random signals, but are elaborated in this Technical Specification in a specific description aimed
at their use for pavement surface profile signals.
NOTE The user of this Technical Specification should be aware that spectral analysis as specified in this document
cannot express all characteristics of the surface profile under study. In particular, the effects of asymmetry of the profile,
e.g. the difference of certain functional qualities for “positive” and “negative” profiles cannot be expressed by the power
spectral density, as it disregards any asymmetry of the signal. (See Annex F.)
2 Normative references
The following referenced documents are indispensable for the application 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 13473-2:2002, Characterization of pavement texture by use of surface profiles — Part 2: Terminology and
basic requirements related to pavement texture profile analysis
ISO 13473-3, Characterization of pavement texture by use of surface profiles — Part 3: Specification and
classification of profilometers
IEC 61260, Electroacoustics — Octave-band and fractional-octave-band filters
3 Terms and definitions
For the purpose of this document, the terms and definitions given in ISO 13473-2:2002 and the following apply.
To assist the users, the most relevant terms and definitions from ISO 13473-2:2002 have been copied into this
Technical Specification.
3.1
(texture) wavelength
λ
quantity describing the horizontal dimension of the amplitude variations of a surface profile
NOTE 1 (Texture) wavelength is normally expressed in metres (m) or millimetres (mm).
NOTE 2 Wavelength is a quantity commonly used and accepted in electrotechnical and signal processing vocabularies.
Since many users of this Technical Specification may not be accustomed to using the term wavelength in pavement
applications, and because electrical signals are often used in the analyses of road surface profiles, there is a possibility of
confusion. Hence, the expression “texture wavelength” is preferred here to make a clear distinction in relation to other
applications
NOTE 3 The profile may be considered as a stationary, random function of the distance along the surface. By means of
a Fourier analysis, such a function may be mathematically represented as an infinite series of sinusoidal components of
various frequencies (and wavelengths), each having a given amplitude and initial phase. For typical and continuous
surface profiles, a profile analysed by its Fourier components contains a continuous distribution of wavelengths. The
texture wavelength in ISO 13473 is the reciprocal of the spatial frequency, the unit of which is reciprocal metre (equivalent
to cycles per metre). See also 3.14.
NOTE 4 The wavelengths may be represented physically as the various lengths of periodically repeated parts of the
profile.
3.2
profile sampling
selection of representative parts of a road surface of which the profile will be measured
3.3
profilometer
device used for measuring the profile of a pavement surface
NOTE Current designs of profilometers used in pavement engineering include, but are not limited to, sensors based
on laser, light sectioning, needle tracer and ultrasonic technologies.
3.4
measurement speed
v
speed at which the profilometer sensor traverses the surface to be measured
NOTE Measurement speed is normally expressed in kilometres per hour (km/h) or metres per second (m/s).
3.5
digital signal sampling
determination of discrete measurement values of a signal at regularly spaced data points (and the subsequent
conversion of these values into digital code)
NOTE In this generic definition of digital signal sampling, the regular spacing of the data points may be applied either
in the time or in the spatial domain, depending on the domain (time or space) in which the signal is captured.
3.6
sampling interval
distance between two adjacent data points on the surface, which is equal to the measurement speed divided
by the sampling frequency of the sensor
NOTE Sampling interval is normally expressed in millimetres (mm).
2 © ISO 2008 – All rights reserved

3.7
profile measurement length
l
p
length of an uninterrupted profile measurement
NOTE Profile measurement length is normally expressed in metres (m) or millimetres (mm).
3.8
repetition interval
r
distance between the beginning of two consecutive profile measurement lengths, the latter as defined in 3.7
NOTE Repetition interval is normally expressed in metres (m).
3.9
evaluation length
l
length of a sample from a profile which has been or is to be analysed
NOTE 1 The evaluation length may or may not be equal to the profile measurement length (but never greater).
NOTE 2 Evaluation length is normally expressed in metres (m) or millimetres (mm).
3.10
drop-out
measured point (sample) on the profile which is recognized as invalid, and which is usually discarded in the
subsequent data processing
3.11
drop-out rate
percentage (%) of measured points within the evaluation length which are recognized as being invalid
3.12
zero-mean, slope-suppressed profile curve
Z(x)
profile curve, Z(x), for which the mean level of the profile over the evaluation length has been brought to zero
and for which long-wavelength trends have been removed
NOTE 1 To obtain a profile curve useful for mathematical calculations, it is necessary to remove any slope or
long-wavelength component (slope suppression), as well as to bring the mean level of the profile over the evaluation
length to zero (offset suppression). This can be accomplished by subtracting a least-squares fit from the profile, see 9.2.
The resulting mean line of the profile is then at zero level. See illustration in Figure 1.
NOTE 2 The features in Figure 1 are exaggerated in order to make the illustration clearer. If subtracting a
least-squares fit from the profile, the two steps from left to right in the figure are performed in one operation (which can be
performed also by high-pass filtering).
Key
1 vertical distance
2 horizontal distance
3 original profile
4 0 level
5 slope suppression applied
6 offset suppression applied
Figure 1 — Illustration of slope and offset suppressions
3.13
surface profile spectrum
texture spectrum
unevenness spectrum
spectrum obtained when a profile curve has been analysed by either digital or analogue filtering techniques in
order to determine the magnitude of its spectral components at different wavelengths (3.1) or spatial
frequencies (3.14)
NOTE A texture spectrum presents the magnitude of each spectral component as a function of either texture
wavelength or spatial frequency.
3.14
spatial frequency
inverse of (texture) wavelength
−1
NOTE 1 Spatial frequency is normally expressed in reciprocal metres (m ); see also 3.1, Note 3.
NOTE 2 The term “frequency” used in the time domain, more precisely “temporal frequency”, corresponds to “spatial
frequency” in the space domain.
3.15
surface (texture) profile level
L
tx,λ
logarithmic transformation of an amplitude representation of a surface profile curve Z(x), the latter expressed
as a root mean square value
EXAMPLE L denotes the texture profile level for the one-third-octave band having a centre wavelength of
tx,80
80 mm, see Table 1 in ISO 13473-2:2002.
NOTE 1 The texture profile level can be expressed by the following equation:
aa
λλ
L or L==10 lg 20 lg dB (1)
tx,λ
TX,λ
a
a
ref
ref
4 © ISO 2008 – All rights reserved

where
−6
L is the texture profile level in one-third-octave bands (ref. 10 m), in decibels;
tx,λ
−6
L is the texture profile level in octave bands (ref. 10 m), in decibels;

TX,λ
a is the root mean square value of the vertical displacement of the surface profile, in metres;
λ
−6
a is the reference value (= 10 m);
ref
λ is the subscript indicating a value obtained with a one-third-octave-band or octave-band filter having centre
wavelength λ.
NOTE 2 Octave-band and one-third-octave-band filters are specified in 4.4 of ISO 13473-2:2002.
NOTE 3 Texture amplitudes expressed as root-mean-square values, whether filtered or not, may have a range of
-5 -2
several magnitudes, typically 10 m to 10 m. Spectral characterization of signals is used frequently in studies of
acoustics, vibrations and electrotechnical engineering. In all those fields, it is most common to use logarithmic amplitude
scales. The same approach is preferred in this part of ISO 13473.
NOTE 4 Texture profile levels in practical pavement engineering typically range from 20 dB to 80 dB with these
definitions.
3.16
power spectral density
PSD
quantity expressing the power contained in a signal per unit frequency or per unit wavelength as a function of
frequency or wavelength
NOTE 1 In the case of a bandwidth filtered signal in the time domain, the PSD may be defined as the limit value of the
time averaged squared signal within a certain frequency interval divided by the bandwidth of this frequency interval when
the bandwidth approaches zero and the averaging time goes to infinity, resulting in the spectrum being presented in terms
of squared amplitude per unit frequency, as expressed by Equation (2).
T
X=∆lim xf( ,f ,t) dt (2)
PSD 0
∫
()∆fT
∆→fT0, →∞
where
X is the power spectral density of a time signal x;
PSD
∆f is the bandwidth of the frequency interval in hertz, Hz;
T is the averaging time in seconds, s.
NOTE 2 In the case of a Discrete Fourier Transform of a sampled signal, the PSD may be defined as the squared
magnitude of the components of the Fourier series divided by the effective bandwidth of the (narrow) bands of the Fourier
spectrum (see 9.4)
NOTE 3 In the case of spectral analysis of a pavement surface profile, the signal is not a function of time but of
evaluation length l. The Power Spectral Density may then be given as a function of the spatial frequency or the (texture)
2 −1 3 2
wavelength and will be expressed in the unit m /m = m or in the unit m /mm, respectively.
NOTE 4 The word “Power” in this designation originates from electric and acoustic signal terminology where signals
incorporate actual power and where the squared amplitude is a measure of this power.
4 Basic outline of methodologies of spatial frequency analysis
Principally, there are three alternative methods to obtain a spatial frequency spectrum in constant-percentage
bandwidth bands of octave- or one-third-octave width. These three methods are:
Method 1 –  analogue constant-percentage bandwidth filtering;
Method 2 –  digital constant-percentage bandwidth filtering;
Method 3 – constant narrow bandwidth frequency analysis by means of Discrete Fourier Transform,
followed by a transformation of the narrow band spectrum to an octave- or one-third-
octave-band spectrum.
All three methods may be expected to give equivalent results (within the confidence intervals arising from
measurement and analysis uncertainty), on condition that the signal quality is high (among other things: free
of drop-outs), and that in each of the methods, all signal processing components fulfil the requirements
specified in this Technical Specification. If, however, the signal is not free from drop-outs, Method 1 is not
recommended because it does not include the possibility for treatment of drop-outs, which may lead to
erroneous results.
Method 2 and 3 will produce fully equivalent results. Method 3 includes more steps than Method 2, but may
offer greater flexibility in the choice of analysis parameters.
The three alternative methods are shown in the scheme of Figure 2. The left path shows the steps for
analogue constant-percentage bandwidth filtering, the middle path shows the steps for digital constant-
percentage bandwidth filtering and the right path shows the steps for analysis using the Discrete Fourier
Transform.
NOTE 1 In the stepwise approach of Method 2, the steps of “digital sampling” and “digital filtering” may be integrated.
NOTE 2 The different steps of Methods 2 and 3 may be implemented in hardware as well as in software.
6 © ISO 2008 – All rights reserved

Figure 2 — Scheme for spectral analysis with reference to clauses and subclauses where the subject
is discussed
5 Sampling of surface profiles
5.1 Sampling of road sections
The most common and preferred way of sampling the surface profile of a road section is along a straight line
in the longitudinal direction of the road. Alternatively, the profilometer may follow other trajectories, adapted to
the nature of the survey, e.g. transverse and oblique lines, circles, spirals or sinusoids. Sampling along
longitudinal lines may be carried out either in the left or the right wheel track or in between wheel tracks.
In any case, the exact shape and position of the sampling trajectory shall be noted and reported accurately.
The spectral analysis shall only be performed on data sets which are derived from a single type of trajectory.
The required evaluation length depends on the frequency analysis to be performed. This leads to the following
requirements for the evaluation length l:
l W 5λ  for octave bands
max
(3)
l W 15λ   for one-third-octave bands
max
whereλ is the longest (one-third-) octave-band-centre wavelength used in the spectral analysis.
max
NOTE These requirements imply that the octave-band levels, respectively one-third-octave band levels, determined
over these evaluation lengths will be within a 95%-confidence interval of approximately ± 3 dB around the true band levels
(that would result from an infinitely long evaluation length).
For sampling of test sections in the longitudinal direction, the following procedure is recommended.
Several profile measurements distributed over the length of the road section shall be carried out. Each profile
measurement length and/or evaluation length shall be large enough to meet the requirement for the maximum
wavelength of Equation (3). The measured profiles shall be evenly distributed along the test section.
The number of profile measurements shall be such that the surface characteristics are well represented by the
measured parts of the test section. The profiles measured shall be analysed separately. When the profiles
measured constitute a representative sample from the test section under consideration, the relative standard
deviation may be regarded as an estimate of the degree of variation of the surface characteristics along the
test section.
It is recommended that each evaluation length be at least 1 m; such an evaluation length enables a one-third-
octave-band λ of approximately 0,08 m, which is sufficient to cover the macrotexture range.
max
EXAMPLE See Figure 3.
length of test section l
r
longest (texture) wavelength λ
max
number of profile measurements N
p
evaluation length l
profile measurement length l
p
l
r
repetition interval r=
N
p
8 © ISO 2008 – All rights reserved

The number of profile measurements N with profile measurement length l can each be divided into parts with evaluation
p p
length l.
Figure 3 — Test section of length l measured with a repetition interval r
r
5.2 Measurement of laboratory samples
When testing road surface samples in the laboratory, it is advisable to use the largest samples available and
to make maximum use of the dimensions of the sample. Rectangular samples should be scanned by the
profilometer along parallel lines. The evaluation length l will be equal to the length of one uninterrupted
scanned line.
Round samples may be scanned along the diameter or along a spiral or circular trajectory. The evaluation
length l will be equal to the length of the uninterrupted scanned trajectory.
The relationship between the evaluation length l and the longest centre wavelength (λ ) to be used in the
max
spectral analysis according to Equation (3) is also applicable in the case of laboratory sample testing.
NOTE It is advisable to maintain a distance between parallel sampling lines or between the subsequent parts of a
spiral trajectory such that the digital samples on one line or part of the trajectory can be considered to be statistically
independent from the digital samples on neighbouring lines, in relation to the range of wavelengths included in the spectral
analysis.
6 General principles and requirements
6.1 Requirements concerning profilometers
The profilometer used to trace and/or sample the pavement texture irregularities shall comply with all
requirements specified in ISO 13473-3 that are applicable to the wavelength range class under observation. If
several wavelength range classes are being observed, the strictest requirements of these ranges shall be
fulfilled.
6.2 Conversion of spatial frequencies to temporal frequencies
6.2.1 General
When sampling a texture with a measurement speed v (in m/s), the signal obtained will be a function of time.
−1
The frequencies within the time signal are defined as temporal frequencies f (in Hz or s ). The temporal
tp
−1
frequency is related to the spatial frequency f (in m ) according to:
sp
f =vf (4)
tp sp
A relative change in speed ∆v / v will cause a relative change in temporal frequency ∆f / f given by:
tp tp
∆ f
∆v
tp
= (5)
f v
tp
The resulting variation of the temporal frequency will cause analysis errors. There are two possible ways to
control these errors, which are discussed in the following two sub-clauses.
6.2.2 Minimization of speed variations
Variations in speed shall be slow in comparison to the surface amplitude variations to be detected. Therefore,
the maximum frequency of the speed variations as a function of time shall be less than 10 % of the minimum
temporal frequency (in Hz) to be analysed.
As well for constant-percentage bandwidth filtering (Methods 1 and 2) as for constant narrow bandwidth
frequency analysis followed by conversion to a constant-percentage bandwidth spectrum (Method 3) the
amplitude of the speed variations shall comply with the following requirements concerning the maximum
relative speed variation over one evaluation length:
For octave-band analysis: ∆v / v shall be smaller than or equal to 10 %

For one-third-octave-band analysis: ∆v / v shall be smaller than or equal to 5 %

NOTE The maximum values of ∆v / v are chosen such that the maximum error in the power per frequency band

resulting from the speed variations will normally not exceed 0,4 dB for a continuous texture spectrum. Larger errors may
occur, however, for surfaces with irregular frequency spectra, e.g. grooved pavements (see Annex C).
6.2.3 Real time compensation for speed variations during measurement
An alternative for minimization of speed variations is to compensate for the speed variations and the resulting
frequency variations during the execution of the measurement. This shall be done in the following way.
In order to acquire a correct digital representation of the surface profile as a function of the measured distance,
it is necessary to take samples at constant sampling intervals ∆x along the measurement trajectory. When
sampling at a measurement speed v, the signal obtained will be a function of time. For a given temporal
sampling frequency f , the temporal sampling intervals ∆t = 1/f will produce spatial sampling intervals ∆x
tp,s tp,s
according to:
v
∆xt=∆⋅v= (6)
f
tp,s
When the speed is constant, the temporal sampling intervals ∆t will be converted into constant spatial
sampling intervals ∆x. If the speed shows variations, the spatial sampling intervals will vary as well.
This can be prevented by applying a speed dependent sampling frequency. Thus, speed variations are
compensated by proportional variations in the temporal sampling frequency so that the resulting spatial
sampling intervals remain constant. Speed dependent sampling can be achieved by using a speed dependent
signal, e.g. derived from the drive mechanism of a measurement vehicle, to control the sampling frequency
generator.
If compensation for speed variations during the execution of the measurement is not possible, the
compensation may also be carried out during the processing of the measured data according to the method
indicated in Annex D.
10 © ISO 2008 – All rights reserved

6.3 Drop-outs
The measurements on a particular pavement shall be considered valid only if the drop-out rate for the
evaluation length in question is not more than 10 % and linear interpolation is used to replace the invalid
samples.
Several drop-outs in a series may occur, as is illustrated in Figure 4. When a series of invalid samples is
preceded and followed by valid samples, each of the invalid samples shall be replaced by an interpolated
value z according to Equation (7):
i
zz−
nm
z=−im+z (7)
()
im
nm−
where
i is the sample number where the value is invalid;
m is the sample number of the nearest valid value before i;
n is the sample number of the nearest valid value after i;
z is the interpolated value for sample i;
i
z is the value of sample m;
m
z is the value of sample n.
n
When the invalid sample(s) constitute(s) the beginning or the end of a sampled profile, the invalid samples
shall be replaced by the value of the nearest valid sample. This method of extrapolation shall be limited to a
maximum length at either side of the sampled profile data series equal to the shortest centre wavelength used
in the spectral analysis.
If interpolation or extrapolation is not used, the last reading before the drop-out(s) shall be used as a
substitute for the drop-out value(s). In such a case, the drop-out rate shall not exceed 5 %.
Measurements with higher drop-out rates than the allowable values shall be discarded.
NOTE For the evaluation of road surface singularities (such as joints), such singularities may be intentionally
included in the analysis, on condition that no invalid readings of the sensor occur.
Key
1 drop-out
2 sample number
NOTE In this case, there are three intermediate consecutive drop-outs, which are linearly interpolated between the
samples at position m and n, and one extreme drop-out, which is extrapolated from the preceding sample.
Figure 4 — Illustration of interpolation and extrapolation of drop-outs
6.4 Anti-aliasing filtering
If digital sampling is involved in the spectral analysis method, aliasing errors (see Annex B) may occur. In
order to avoid such errors during the spectral analysis, the analogue signal representing the surface profile
shall be filtered before digital sampling with a low-pass filter with a cut-off frequency lower than half the
sampling frequency.
The filter characteristics shall be such that there is a flat response within 0,4 dB up to the highest frequency to
be analysed. The attenuation of the filter at half the sampling frequency shall be 60 dB or more.
If the analogue signal is inherently filtered by the detection process of the profilometer itself (such as the
filtering by the spot-size of a laser beam) or by a natural high frequency roll-off, the combined characteristics
of this inherent filtering and the anti-aliasing filter shall meet the above mentioned requirements.
The requirements with respect to the filter characteristics may be alleviated if it can be determined from
preliminary information that the surface profile spectrum will be continuous and smooth in the frequency range
of interest.
6.5 Digital sampling
When the spectral analysis method involves digital sampling, it shall be performed at spatial sampling
intervals ∆x that are determined according to ISO 13473-3 for the shortest wavelength involved in the spectral
analysis.
12 © ISO 2008 – All rights reserved

The required temporal sampling frequency f (in Hz) for a moving profilometer can be obtained from the
tp, s
requirement concerning the spatial sampling interval ∆x (in m) and the measurement speed of the profilometer
v (in m/s) by:
v
f = (8)
tp,s
∆x
Sampling shall be performed with constant (spatial) sampling intervals. To maintain a constant sampling
interval, it is recommended that the temporal sampling frequency be adjusted continuously to the
measurement speed (see Annex D). If this method of compensation is not possible, variations in the
measurement speed will cause analysis errors, which shall remain relatively small. If digital sampling is used
to derive an octave- or one-third-octave-band spatial frequency spectrum, the requirements for the maximum
relative speed variation of 6.1 apply.
If the final result of the narrow band analysis by means of Discrete Fourier Transform is a narrow band
spectrum, only the method of compensation for the speed variations shall be used to achieve a constant
spatial sampling interval.
7 Spectral analysis in constant-percentage bandwidth bands (octave- or one-third-
octave bands) by analogue filtering (Method 1)
The method of spectral analysis by analogue constant-percentage bandwidth filtering shall only be used if it
can be verified that the measurement signal from the profilometer is completely free of drop-outs. Such
verification may consist of detailed visual inspection of the (analogue) recorded profiles or the use of a drop-
out detection system on the profilometer.
The analogue signal obtained by tracing the surface profile may be fed directly into analogue octave- or third-
octave-band filters. These filters, used for frequency analysis in constant-percentage bandwidth bands, shall
have centre texture wavelengths and centre spatial frequencies according to ISO 13473-2:2002 (4.4 and
Table 1), which is established so as to numerically correspond to the bands specified in IEC 61260. The upper
and lower cut-off (−3 dB) frequencies of each band, as well as the shape of the filter frequency response shall
conform to IEC 61260.
Frequency analysis by analogue filtering may be applied directly to the time signal resulting from the
measurement of the surface profile with a profilometer with a measurement speed v. The temporal frequency
and the pass band of the filters shall be adapted to the measurement speed. If f is the mid-band
sp,m
frequency of the required spatial frequency band, the temporal centre frequency f of the filter shall be:
tp, m
fv=f (9)
tp,m sp,m
For standardized band pass filters with a fixed series of temporal centre frequencies, the speed of the
measurement shall be adjusted such that the filtering corresponds to the preferred spatial frequency bands
(compliant with Table 1 of ISO 13472-2:2002). Using the preferred base-ten system, the measurement shall
be conducted at one of the speeds determined according to Equation (10):
3n
v=⋅3,6 10 km/h for one-octave bands
(10)
n
v=⋅3,6 10 km/h for one-third-octave bands
where n is an integer, the value of which can be freely chosen from the series: …, −2, −1, 0, 1, 2, … in order
to obtain a desired speed.
In Table 1, the one-third-octave-band spatial frequencies are listed with the required temporal frequencies for
three different examples of measurement speeds from the series defined by Equation (10).
Table 1 — List of one-third-octave-band spatial frequencies and the required one-third-octave-band
temporal frequencies for three different measurement speeds
Texture One-third-octave-band One-third-octave-band One-third-octave-band One-third-octave-band
wavelength spatial frequency temporal frequency temporal frequency temporal frequency
at speed 18 km/h at speed 36 km/h at speed 72 km/h

−1
in mm in m in Hz in Hz in Hz
500 2,00 10,0 20,0 40,0
400 2,50 12,5 25,0 50,0
315 3,15 16,0 31,5 63,0
250 4,00 20,0 40,0 80,0
200 5,00 25,0 50,0 100
160 6,30 31,5 63,0 125
125 8,00 40,0 80,0 160
100 10,0 50,0 100 200
80,0 12,5 63,0 125 250
63,0 16,0 80,0 160 320
50,0 20,0 100 200 400
40,0 25,0 125 250 500
31,5 31,5 160 315 630
25,0 40,0 200 400 800
20,0 50,0 250 500 1 000
16,0 63,0 315 630 1 250
12,5 80,0 400 800 1 600
10,0 100 500 1 000 2 000
8,00 125 630 1 250 2 500
6,30 160 800 1 600 3 200
5,00 200 1 000 2 000 4 000
4,00 250 1 250 2 500 5 000
3,15 315 1 600 3 150 6 300
2,50 400 2 000 4 000 8 000
2,00 500 2 500 5 000 10 000
1,60 630 3 150 6 300 12 500
1,25 800 4 000 8 000 16 000
1,00 1 000 5 000 10 000 20 000
0,80 1 250 6 300 12 500 25 000
0,63 1 600 8 000 16 000 32 000
0,50 2 000 10 000 20 000 40 000
0,40 2 500 12 500 25 000 50 000
NOTE Otave-band frequencies are printed in bold.
14 © ISO 2008 – All rights reserved

8 Spectral analysis in constant-percentage bandwidth bands
(octave- or one-third-octave bands) by digital filtering (Method 2)
The method of constant-percentage bandwidth filtering by means of digital filters shall be conducted according
to the following steps:
a) anti-aliasing filtering according to 6.4;
b) digital sampling according to 6.5;
c) interpolation of drop-outs (if needed) according to 6.3;
d) digital constant-percentage bandwidth filtering.
The last step mentioned above shall be performed with digital octave- or one-third-octave-band filters. These
filters shall have centre texture wavelengths and centre spatial frequencies according to ISO 13473-2:2002
(4.4 and Table 1), which are established so as to numerically correspond to the bands specified in IEC 61260.
The upper and lower cut-off (−3 dB) frequencies of each band, as well as the shape of the filter frequency
response shall conform to IEC 61260.
If digital filtering is applied to the sampled time signal resulting from the measurement of the surface profile,
the temporal frequency and the pass-band of the filters shall be adapted to the measurement speed v as
specified in Clause 7, Equation (9) and Equation (10) and examples in Table 1.
9 Spectral analysis in narrow constant bandwidth bands by means of Discrete
(Fast) Fourier Transform methods (Method 3)
9.1 Overview of methodology
The methodology to derive a constant-percentage band
...