SIST EN ISO 16610-22:2026

Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2026)

This document specifies linear spline filters for the filtration of surface profiles. It defines, in particular, how to separate large- and small-scale lateral components of surface profiles.
The concepts presented for closed profiles are applicable to the case of roundness filtration. Where appropriate, these concepts can be extended to generalized closed profiles, especially for surface profiles with re-entrant features.
Examples for the application of the spline filter are given in Annex A. The influence of the tension parameter  on the large-scale lateral component of the profile is shown in Annex B.

Geometrische Produktspezifikation (GPS) - Filterung - Teil 22: Lineare Profilfilter: Spline-Filter (ISO 16610-22:2026)

Dieses Dokument legt lineare Spline-Filter zur Filterung von Oberflächenprofilen fest. Es legt insbesondere fest, wie langwellige und kurzwellige Anteile von Oberflächenprofilen getrennt werden.
Die für geschlossene Profile dargestellten Konzepte sind für den Fall der Rundheitsfilterung anwendbar. Diese Konzepte können gegebenenfalls auf verallgemeinerte geschlossene Profile erweitert werden, insbesondere für Oberflächenprofile mit Wiederholungsmerkmalen.
Beispiele für die Anwendung des Spline-Filters sind in Anhang A angegeben. Der Einfluss der Spannungskenngröße β auf den langwelligen Anteil des Oberflächenprofils ist in Anhang B dargestellt.

Spécification géométrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil linéaires: Filtres splines (ISO 16610-22:2026)

Le présent document spécifie les filtres splines linéaires pour le filtrage des profils de surface. Il définit, en particulier, la manière de séparer les composantes latérales à grande et à petite échelle de profils de surface.
Les concepts présentés pour les profils fermés s’appliquent au cas du filtrage de circularité. Le cas échéant, ces concepts peuvent être étendus aux profils fermés généralisés, en particulier pour les profils de surface présentant des éléments réentrants.
Des exemples pour l’application du filtre spline sont donnés à l'Annexe A. L’influence du paramètre de tension β sur la composante latérale à grande échelle du profil est montré à l'Annexe B.

Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 22. del: Filtri linearnih profilov: utorni filtri (ISO 16610-22:2026)

Ta dokument določa linearne spline filtre za filtracijo površinskih profilov. Posebej opredeljuje, kako ločiti velike in majhne lateralne komponente površinskih profilov.
Predstavljeni koncepti za zaprte profile so uporabni v primeru filtracije okroglosti. Kjer je primerno, se lahko ti koncepti razširijo na posplošene zaprte profile, zlasti za površinske profile s ponavljajočimi se značilnostmi.
Primeri uporabe spline filtra so podani v Prilogi A. Vpliv napetostnega parametra na veliko lateralno komponento profila je prikazan v Prilogi B.

General Information

• Status: Published
• Public Enquiry End Date: 30-Jan-2025
• Publication Date: 08-Apr-2026
• ICS: 17.040.20 - Properties of surfaces
• ICS: 17.040.40 - Geometrical Product Specification (GPS)
• Technical Committee: ISEL - Mechanical elements
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 31-Mar-2026
• Due Date: 05-Jun-2026
• Completion Date: 09-Apr-2026
• Ref Project: EN ISO 16610-22:2026 - Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2026)

Relations

• Revises: SIST EN ISO 16610-22:2015 - Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2015)
• Effective Date: 04-Oct-2023

Overview

FprEN ISO 16610-22 (ISO/DIS 16610-22:2024; FDIS 16610-22:2025) defines linear spline filters for the filtration of surface profiles within the Geometrical Product Specifications (GPS) system. The standard explains how to separate a profile into large-scale (form/waviness) and small-scale (roughness) lateral components using spline-based linear filters. Spline filters are linear, use a weighting function (convolution) and have a defined transmission characteristic that transmits 50% of the amplitude for sinusoidal profiles at the cut-off wavelength.

Key topics

• Filter concept and scope
  • Linear spline filters for both open and closed profiles (closed profiles applicable to roundness).
  • Separation of large- and small-scale lateral components without altering the reconstructibility of the profile.
• Filter equations and implementation
  • Definitions of weighting functions and convolution-based computation for the large-scale component.
  • Determination of small-scale lateral component by subtraction.
  • Sections on practical implementation and filter designation to standardize reporting.
• Transmission characteristics
  • Transmission defined as the Fourier transform of the weighting function.
  • Cut-off wavelength (nesting index) is the wavelength at which 50% of sinusoidal amplitude is transmitted.
  • Separate transmission descriptions for large- and small-scale components.
• Parameters
  • Nesting index / cut-off wavelength and tension parameter β (controls spline tension and filter behavior).
  • Series of recommended nesting index values and guidance on choosing β.
• Support material
  • Informative annexes with examples, influence of β, and relationships to GPS and filtration matrix models.

Applications

• Surface metrology and roughness analysis - to extract roughness, waviness, and form components for inspection and specification.
• Roundness and circular profile filtration - closed-profile (roundness) use via undulations-per-revolution (UPR) and cut-off frequency.
• Quality control, manufacturing process monitoring, and certification in precision engineering industries.
• Instrument and software vendors implementing standardized profile filters in profilometers, coordinate measuring machines (CMMs), and analysis tools.

Who should use it

• Metrology engineers and lab technicians performing surface texture analysis.
• Quality assurance and process engineers defining specification limits.
• Measurement equipment and software developers implementing GPS-compliant filters.
• Standards bodies and conformity assessment organizations aligning specifications across supply chains.

Related standards

• ISO 16610 series (general filtration methods), ISO 16610-1, ISO 16610-20
• ISO 14638 (GPS matrix model), ISO 8015 (fundamental GPS rules), ISO 14253-1 (decision rules)

Keywords: ISO 16610-22, spline filters, linear profile filters, surface profile filtration, GPS, cut-off wavelength, transmission characteristic, nesting index, surface metrology.

Standards Content (Sample)

SLOVENSKI STANDARD
01-maj-2026
Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 22. del: Filtri
linearnih profilov: utorni filtri (ISO 16610-22:2026)
Geometrical product specifications (GPS) - Filtration - Part 22: Linear profile filters:
Spline filters (ISO 16610-22:2026)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 22: Lineare Profilfilter: Spline-
Filter (ISO 16610-22:2026)
Spécification géométrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil
linéaires: Filtres splines (ISO 16610-22:2026)
Ta slovenski standard je istoveten z: EN ISO 16610-22:2026
ICS:
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 16610-22
EUROPEAN STANDARD
NORME EUROPÉENNE
March 2026
EUROPÄISCHE NORM
ICS 17.040.40 Supersedes EN ISO 16610-22:2015
English Version
Geometrical product specifications (GPS) - Filtration - Part
22: Linear profile filters: Spline filters (ISO 16610-
22:2026)
Spécification géométrique des produits (GPS) - Filtrage Geometrische Produktspezifikation (GPS) - Filterung -
- Partie 22: Filtres de profil linéaires: Filtres splines Teil 22: Lineare Profilfilter: Spline-Filter (ISO 16610-
(ISO 16610-22:2026) 22:2026)
This European Standard was approved by CEN on 2 March 2026.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 16610-22:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 16610-22:2026) has been prepared by Technical Committee ISO/TC 213
"Dimensional and geometrical product specifications and verification" in collaboration with Technical
Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the
secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by September 2026, and conflicting national standards
shall be withdrawn at the latest by September 2026.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 16610-22:2015.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 16610-22:2026 has been approved by CEN as EN ISO 16610-22:2026 without any
modification.
International
Standard
ISO 16610-22
Second edition
Geometrical product specifications
2026-03
(GPS) — Filtration —
Part 22:
Linear profile filters: Spline filters
Spécification géométrique des produits (GPS) — Filtrage —
Partie 22: Filtres de profil linéaires: Filtres splines
Reference number
ISO 16610-22:2026(en) © ISO 2026

ISO 16610-22:2026(en)
© ISO 2026
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
ISO 16610-22:2026(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristics of the spline filter for open profiles . 3
4.1 General .3
4.2 Filter equations .3
4.2.1 Determination of the large-scale lateral component .3
4.2.2 Determination of the small-scale lateral component .4
4.3 Transmission characteristics .5
4.3.1 Transmission characteristic for the large-scale lateral component .5
4.3.2 Transmission characteristic for the small-scale lateral component .6
5 Characteristics of the spline filter for a closed profile . 7
5.1 General .7
5.2 Filter equations .7
5.2.1 Determination of the large-scale lateral component .7
5.2.2 Determination of the small-scale lateral component .8
5.3 Transmission characteristics .8
5.3.1 Transmission characteristic for the large-scale lateral component .8
5.3.2 Transmission characteristic of the small-scale lateral component .9
6 Series of nesting index values . 10
7 Tension parameter β . 10
8 Implementation . . 10
9 Filter designation .11
Annex A (informative) Examples for the application of the spline filter .12
Annex B (informative) Influence of the tension parameter β .15
Annex C (informative) Relationship to the filtration matrix model .21
Annex D (informative) Relationship to the GPS matrix model .22
Bibliography .23

iii
ISO 16610-22:2026(en)
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of
patents which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
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 213, Dimensional and geometrical product
specifications and verification, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This second edition cancels and replaces the first edition (ISO 16610-22:2015), which has been technically
revised.
The main changes compared to the previous edition are as follows:
— correction of the transmission characteristics, Formulae (8) and (9) in the first edition, and correction of
the example Figure C.4 in the first edition;
— addition of an informative Annex B to show the influence of the tension parameterβ ;
— addition of the transmission characteristics for closed profiles that apply to the case of roundness
filtration.
A list of all parts in the ISO 16610 series can be found on the ISO website.
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
ISO 16610-22:2026(en)
Introduction
This document is a geometrical product specification (GPS) standard and is to be regarded as a general GPS
standard (see ISO 14638). It influences chain links C and E in the GPS matrix structure.
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this document
is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and the default decision
rules given in ISO 14253-1 apply to the specifications made in accordance with this document, unless
otherwise indicated.
For more information on the relationship of this document to the filtration matrix model, see Annex C.
For more detailed information on the relation of this document to other standards and the GPS matrix model,
see Annex D.
This document develops the terminology and concepts of linear spline filters for surface profiles. Linear
spline filters for surface profiles have a transmission of 50 % for sinusoidal surface profiles with wavelengths
equal to the cut-off wavelength. They separate the large- and small-scale lateral components of surface
profiles in such a way that the surface profiles can be reconstructed without altering. Depending on the
selected nesting index and tension parameter, linear spline filters offer one method for F-operation.

v
International Standard ISO 16610-22:2026(en)
Geometrical product specifications (GPS) — Filtration —
Part 22:
Linear profile filters: Spline filters
1 Scope
This document specifies linear spline filters for the filtration of surface profiles. It defines, in particular, how
to separate large- and small-scale lateral components of surface profiles.
The concepts presented for closed profiles are applicable to the case of roundness filtration. Where
appropriate, these concepts can be extended to generalized closed profiles, especially for surface profiles
with re-entrant features.
Examples for the application of the spline filter are given in Annex A. The influence of the tension parameter
β on the large-scale lateral component of the profile is shown in Annex B.
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 16610-1:2015, Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic concepts
ISO 16610-20:2015, Geometrical product specifications (GPS) — Filtration — Part 20: Linear profile filters:
Basic concepts
ISO/IEC Guide 99, International vocabulary of metrology — Basic and general concepts and associated terms
(VIM)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1, ISO 16610-20,
ISO/IEC Guide 99 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/
3.1
surface profile
line resulting from the intersection between a surface portion and an ideal plane
Note 1 to entry: The orientation of the ideal plane is usually perpendicular to the tangent plane of the surface portion.
Note 2 to entry: See ISO 17450-1:2011, 3.3 and 3.3.1, for the definition of an ideal plane.
[SOURCE: ISO 16610-1:2015, 3.1.2, modified — Note 2 to entry replaced.]

ISO 16610-22:2026(en)
3.1.1
open profile
finite length surface profile (3.1) with two ends
Note 1 to entry: An open profile has a compact support, i.e. within a certain interval the height values of an open
profile can be equal to any real number. Outside the interval, the height values of an open profile are set to zero.
[SOURCE: ISO 16610-1:2015, 3.7, modified — Note 1 to entry replaced.]
3.1.2
unbounded open profile
infinite length surface profile (3.1) without ends
Note 1 to entry: In this document, the term “unbounded” refers to the X-axis.
Note 2 to entry: The concept of the unbounded open profile is ideal and does not apply to real surface profiles.
3.1.3
closed profile
connected finite length surface profile (3.1) without ends
Note 1 to entry: A closed profile is a closed curve which is periodic with the finite period length L.
Note 2 to entry: A typical example of a closed profile is one from a roundness measurement.
[SOURCE: ISO 16610-1:2015, 3.8, modified — Note 1 to entry replaced. Note 2 to entry added.]
3.2
linear profile filter
profile filter which separates surface profiles (3.1) into large- and small-scale lateral components and is also
a linear function
Note 1 to entry: If F is a function and X and Y are surface profiles, and if a and b are independent from X and Y, then F
being a linear function implies F (a X + b Y) = a F(X) + b F(Y).
[SOURCE: ISO 16610-20:2015, 3.1, modified — In definition “profiles” replaced by “surface profiles” and “long
wave” and “short wave” replaced by “large-scale lateral” and “small-scale lateral”; Note 1 to entry replaced.]
3.3
weighting function
function to calculate large-scale lateral components by convolution of the surface profile heights with this
function
Note 1 to entry: The convolution (see ISO 16610-20:2015, 4.1) performs a weighted moving average of the surface
profile heights. The weighting function, reflected at the X-axis, defines the weighting coefficients for the averaging
process.
3.4
transmission characteristic

characteristic that indicates the amount by which the amplitude of a sinusoidal surface profile is attenuated
as a function of its wavelength
Note 1 to entry: The transmission characteristic for the large-scale lateral component is the Fourier transformation of
the weighting function (3.3).
[SOURCE: ISO 16610-20:2015, 3.4]

ISO 16610-22:2026(en)
3.5
cut-off wavelength
λ
c
wavelength of a sinusoidal surface profile of which 50 % of the amplitude is transmitted by the profile filter
Note 1 to entry: Linear profile filters are identified by the filter type and the cut-off wavelength value.
Note 2 to entry: The cut-off wavelength is the nesting index for linear profile filters.
[SOURCE: ISO 16610-20:2015, 3.5, modified — In Note 2 to entry “recommended” deleted.]
3.6
undulations per revolution
UPR
number of sinusoidal undulations contained in a closed profile (3.1.3)
Note 1 to entry: In this document, UPR is a frequency and is denoted by f.
3.7
cut-off frequency
f
c
frequency, in UPR, of a sinusoidal closed profile (3.1.3) of which 50 % of the amplitude is transmitted by the
profile filter
3.8
spline
linear combination of piecewise polynomials, with a smooth fit between the pieces
Note 1 to entry: The degree of the spline is equal to the degree of the polynomial of the highest degree used.
4 Characteristics of the spline filter for open profiles
4.1 General
In this clause, the filter equations and transfer characteristics of the spline filter for uniformly sampled open
profiles are considered.
4.2 Filter equations
4.2.1 Determination of the large-scale lateral component
For the determination of the large-scale lateral component of an open profile, the spline filter is defined by
Formula (1):
ISO 16610-22:2026(en)
IP 1 Qw z (1)

nnnn nnnn11
where
12 10  0
 
 
 25 41 
11 00
 
 
 
 
12 1  1464 1 
 
 
 
 
PQ 00 ,  00 ,
nnn nn
 
 
 
 
 12 1  1464 1
 
 
 
00 11  1452
   
 
00 1 221


and
n
is the number of sampled values of the open profile;
is the identity matrix of dimension nn× ;
I
nn×
z is the vector of dimension n×1 of the open profile uniformly sampled within its two ends;

n×1
w is the vector of dimension n×1 of the large-scale lateral comp
...