IEC 62754:2017

IEC 62754 ®
Edition 1.0 2017-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Computation of waveform parameter uncertainties

Calcul des incertitudes des paramètres des formes d'onde

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IEC 62754 ®
Edition 1.0 2017-05
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Computation of waveform parameter uncertainties

Calcul des incertitudes des paramètres des formes d'onde

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.20 ISBN 978-2-8322-4345-9

– 2 – IEC 62754:2017  IEC 2017
CONTENTS
FOREWORD . 4
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 Waveform measurement . 16
4.1 General . 16
4.2 Waveform parameters . 17
4.3 Waveform measurement process . 17
4.3.1 General . 17
4.3.2 General description of the measurement system . 18
5 Waveform and waveform parameter corrections . 19
5.1 General . 19
5.2 Waveform parameter corrections . 19
5.3 Waveform corrections and waveform reconstruction. 20
5.3.1 General . 20
5.3.2 Sample-by-sample correction . 20
5.3.3 Entire waveform correction . 20
6 Uncertainties . 22
6.1 General . 22
6.2 Propagation of uncertainties . 22
6.2.1 General . 22
6.2.2 Uncorrelated input quantities . 23
6.2.3 Correlated input quantities . 23
6.3 Pooled data and its standard deviation. 23
6.4 Expanded uncertainty and coverage factor. 25
6.4.1 General . 25
6.4.2 Effective degrees of freedom . 27
6.5 Entire waveform uncertainties . 28
7 Waveform parameter uncertainties . 29
7.1 General . 29
7.2 Amplitude parameters . 30
7.2.1 State levels. 30
7.2.2 State boundaries . 35
7.2.3 Waveform amplitude (state levels) . 36
7.2.4 Impulse amplitude (state levels) . 37
7.2.5 Percent reference levels (state levels, waveform amplitude) . 37
7.2.6 Transition settling error (state levels, waveform amplitude) . 38
7.2.7 Overshoot aberration (state levels, waveform amplitude) . 38
7.2.8 Undershoot aberration (state levels, waveform amplitude) . 39
7.3 Temporal parameters . 39
7.3.1 Initial instant . 39
7.3.2 Waveform epoch . 40
7.3.3 Reference level instants (percent reference levels, waveform epoch,
initial instant) . 41
7.3.4 Impulse centre instant (impulse amplitude, reference level instants) . 42
7.3.5 Transition duration (reference level instants) . 42

7.3.6 Transition settling duration (reference level instants) . 43
7.3.7 Pulse duration (reference level instants) . 43
7.3.8 Pulse separation (reference level instants) . 43
7.3.9 Waveform delay (advance) (reference level instants) . 44
8 Monte Carlo method for waveform parameter uncertainty estimates . 44
8.1 General guidance and considerations . 44
8.2 Example: state level . 44
Annex A (informative) Demonstration example for the calculation of the uncertainty of
state levels using the histogram mode according to 7.2.1.2. 46
A.1 Waveform measurement . 46
A.2 Splitting the bimodal histogram and determining the state levels . 46
A.3 Uncertainty of state levels . 47
Annex B (informative) Computation of Σ andΣ for estimating the uncertainty of
L Y
state levels using the shorth method according to 7.2.1.3 . 49
Bibliography . 52

Figure 1 – Reference levels, reference level instants, waveform amplitude, and
transition duration for a single positive-going transition . 7
Figure 2 – Overshoot, undershoot, state levels, and state boundaries for a single
positive-going transition . 11
Figure 3 – Creation of measured, corrected, and reconstructed waveforms and the
final estimate of the input signal . 17
Figure 4 – Example of waveform bounds focusing on the trajectories that impact pulse
parameter measurements . 28
Figure 5 – Relationship between selected waveform parameters . 30
Figure A.1 – Waveform obtained from the measurement of a step-like signal from
which the state levels and uncertainties are calculated . 46
Figure A.2 – Histograms of state s1 (a) and state s2 (b) of the step-like waveform
plotted in Figure A.1 . 47
(α)
Figure B.1 – Diagram showing location of waveform elements, y , in Y and Y , and
(β) 1 2
the construction of Y from Y and Y . 49
1 2
Table 1 – Value of the coverage factor k that encompasses the fraction p of the t -
p
distribution for different degrees of freedom (from ISO/IEC Guide 98-3) . 26
Table 2 – Different methods for determining state levels, as given in IEC 60469, and
their uncertainty type and method of computation . 31
Table 3 – Different methods for determining state boundaries and their uncertainty type
and method of computation . 36
Table 4 – Variables contributing to the uncertainty in overshoot . 39
Table 5 – Variables contributing to the uncertainty in the reference level instant . 42
Table A.1 – Uncertainty contributions and total uncertainty for level(s ) determined from
i
histogram modes . 48

– 4 – IEC 62754:2017  IEC 2017
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
COMPUTATION OF WAVEFORM PARAMETER UNCERTAINTIES

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 62754 has been prepared by IEC technical committee 85:
Measuring equipment for electrical and electromagnetic quantities.
The text of this International Standard is based on the following documents:
FDIS Report on voting
85/585/FDIS 85/X588/RVD
Full information on the voting for the approval of this International Standard can be found in
the report on voting indicated in the above table.
This document has been drafted in accordance with the ISO/IEC Directives, Part 2.
The terms used throughout this document which have been defined in Clause 3 are in italic
type.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates
that it contains colours which are considered to be useful for the correct
understanding of its contents. Users should therefore print this document using a
colour printer.
– 6 – IEC 62754:2017  IEC 2017
COMPUTATION OF WAVEFORM PARAMETER UNCERTAINTIES

1 Scope
This document specifies methods for the computation of the temporal and amplitude
parameters and their associated uncertainty for step-like and impulse-like waveforms. This
document is applicable to any and all industries that generate, transmit, detect, receive,
measure, and/or analyse these types of pulses.
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.
IEC 60469:2013, Transitions, pulses and related waveforms – Terms, definitions and
algorithms
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
3.1
aberration region
3.1.1
post-transition aberration region
interval between a user-specified instant and a fixed instant, where the fixed instant is the first
sampling instant succeeding the 50 % reference level instant for which the corresponding
waveform value is within the state boundaries of the state succeeding the 50 % reference
level instant
[SOURCE: IEC 60469:2013, 3.2.1.1, modified – the note 1 to entry has been deleted.]
3.1.2
pre-transition aberration region
interval between a user-specified instant and a fixed instant, where the fixed instant is the first
sampling instant preceding the 50 % reference level instant for which the corresponding
waveform value is within the state boundaries of the state preceding the 50 % reference level
instant
[SOURCE: IEC 60469:2013, 3.2.1.2, modified – the note 1 to entry has been deleted.]

3.2
amplitude
3.2.1
impulse amplitude
difference between the specified level corresponding to the maximum peak (minimum peak) of
the positive (negative) impulse-like waveform and the level of the state preceding the first
transition of that impulse-like waveform
[SOURCE: IEC 60469:2013, 3.2.3.1]
3.2.2
waveform amplitude
difference between the levels of two different states of a waveform
SEE Figure 1.
50 % reference level instant
10 % reference level instant 90 % reference level instant
90 % reference level
S
50 % reference level
10 % reference level
S
Transition occurrence instant
Transition duration
Base state
Waveform epoch
t
IEC
Figure 1 – Reference levels, reference level instants, waveform amplitude, and
transition duration for a single positive-going transition
[SOURCE: IEC 60469:2013, 3.2.3.2, modified – the Note 1 to entry has been deleted and the
reference to Figure 1 has been added.]
3.3
correction
operation that combines the results of the conversion operation with the transfer function
information to yield a waveform that is a more accurate representation of the signal
Note 1 to entry Correction may be effected by a manual process by an operator, a computational process, or a
compensating device or apparatus. Correction shall be performed to an accuracy that is consistent with the overall
accuracy desired in the waveform measurement process.
[SOURCE: IEC 60469:2013, 3.2.4]
Waveform amplitude
Offsett
– 8 – IEC 62754:2017  IEC 2017
3.4
coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain
an expanded uncertainty
Note 1 to entry: A coverage factor, k, is typically in the range 2 to 3.
Note 2 to entry: Coverage factor is also defined as a “number larger than or equal to one by which a combined
standard measurement uncertainty is multiplied to obtain an expanded measurement uncertainty,” (See ISO/IEC
Guide 99:2007, 2.38).
[SOURCE: ISO/IEC Guide 98-3:2008, 2.3.6, modified – the Note 2 to entry has been added.]
3.5
degrees of freedom
in general, the number of terms in a sum minus the number of constraints on the terms of the
sum
[SOURCE: ISO/IEC Guide 98-3:2008, C.2.31]
3.6
impulse response
output signal from an instrument, device, or system that is the result of an input signal, where
this input signal can be described by a unit impulse function, δ(t):
δ(t= 0) = 1
(1)
δ(t≠ 0) = 0
3.7
instant
particular time value within a waveform epoch that, unless otherwise specified, is referenced
relative to the initial instant of that waveform epoch
[SOURCE: IEC 60469:2013, 3.2.13]
3.7.1
initial instant
first sample instant in the waveform
[SOURCE: IEC 60469:2013, 3.2.13.3]
3.7.2
impulse center instant
instant at which a user-specified approximation to the maximum peak (minimum peak) of the
positive (negative) impulse-like waveform occurs
[SOURCE: IEC 60496:2013, 3.2.13.2]
3.7.3
reference level instant
instant at which the waveform intersects a specified reference level
SEE Figure 1.
[SOURCE: IEC 60469:2013, 3.2.13.5, modified – the reference to Figure 1 has been added.]

3.8
interval
set of all values of time between a first instant and a second instant, where the second instant
is later in time than the first
Note 1 to entry: These first and second instants are called the endpoints of the interval. The endpoints, unless
otherwise specified, are assumed to be part of the interval.
[SOURCE: IEC 60469:2013, 3.2.15]
3.9
level
constant value having the same units as y
SEE Figure 1.
Note 1 to entry: y is the signal.
[SOURCE: IEC 60469:2013, 3.2.17, modified – the reference to Figure 1 has been added as
well as the note 1 to entry.]
3.9.1
percent reference level
reference level specified by:
x
y = y + (y − y )
x% 0% 100% 0%
(2)
100%
where
0 % < x < 100 %
y = level of low state
0%
y = level of high state
100%
y , y , and y are all in the same unit of measurement
0% 100% x%
SEE Figure 1.
Note 1 to entry: Commonly used reference levels are: 0 %, 10 % , 50 %, 90 %, and 100 %.
[SOURCE: IEC 60469:2013, 3.2.17.3, modified – the reference to Figure 1 has been added.]
3.10
measurand
quantity intended to be measured
[SOURCE: ISO/IEC Guide 99:2007, 2.3, modified – the notes have been deleted.]
3.11
measurement model
model of measurement
model
mathematical relation among all quantities known to be involved in a measurement
[SOURCE: ISO/IEC Guide 99:2007, 2.48, modified – the notes have been deleted.]

– 10 – IEC 62754:2017  IEC 2017
3.12
measurement uncertainty
uncertainty of measurement
uncertainty
non-negative parameter characterizing the dispersion of the quantity values being attributed
to a measurand, based on the information used
Note 1 to entry Measurement uncertainty is also defined as a “parameter, associated with the result of a
measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand,”
(See ISO/IEC Guide 98-3:2008, 2.2.3).
[SOURCE: ISO/IEC Guide 99:2007, 2.26, modified – the notes have been deleted and the
note 1 to entry has been added.]
3.12.1
standard measurement uncertainty
standard uncertainty of measurement
standard uncertainty
measurement uncertainty expressed as a standard deviation
Note 1 to entry: Standard measurement uncertainty is also defined as an “uncertainty of the results of
measurement expressed as a standard deviation,” ( See ISO/IEC Guide 98-3:2008, 2.3.1).
[SOURCE: ISO/IEC Guide 99:2007, 2.30, modified – the note 1 to entry has been added.]
3.12.2
combined standard measurement uncertainty
combined standard uncertainty
standard measurement uncertainty that is obtained using the individual standard
measurement uncertainties associated with the input quantities in a measurement model
Note 1 to entry: Combined standard uncertainty is also defined as a “standard uncertainty of the result of a
measurement when that result is obtained from the values of a number of other quantities, equal to the positive
square root of a sum of terms, the terms being the variances or covariances of these other quantities weighted
according to how the measurement result varies with changes in these quantities,” (See ISO/IEC Guide 98-3:2008,
2.3.4).
[ISO/IEC Guide 99:2007, 2.31, modified – the note has been deleted and the note 1 to entry
has been added.]
3.12.3
expanded measurement uncertainty
expanded uncertainty
product of a combined standard measurement uncertainty and a factor larger than the number
one
[SOURCE: ISO/IEC Guide 99:2007, 2.35]
Note 1 to entry: Expanded uncertainty is also defined as a “quantity defining an interval about the result of a
measurement that may be expected to encompass a large fraction of the distribution values that could reasonably
be attributed to the measurand,” (See ISO/IEC Guide 98-3:2008,2.3.5).
[SOURCE: ISO/IEC Guide 99:2007, 2.35, modified – the notes have been deleted and the
note 1 to entry has been added.]
3.12.4
instrumental measurement uncertainty
instrumental uncertainty
component of measurement uncertainty arising from a measuring instrument or measuring
system in use
[SOURCE: ISO/IEC Guide 99:2007, 4.24, modified – the term "instrumental uncertainty" has
been added as a synonym and the notes have been deleted.]
3.12.4.1
intrinsic (instrumental) uncertainty
uncertainty of a measuring instrument when used under reference conditions
[SOURCE: IEC 60359:2001, 3.2.10]
3.12.4.2
operating instrumental uncertainty
instrumental uncertainty under the rated operating conditions
[SOURCE: IEC 60359:2001, 3.2.11]
3.13
overshoot
waveform aberration within a post-transition aberration region or pre-transition aberration
region that is greater than the upper state boundary for the associated state level
SEE Figure 2.
Post-transition overshoot
Upper (S )
Post-transition undershoot
S
Lower (S )
Post-transition aberration
region
Pre-transition aberration
region
Upper (S )
S
Lower (S )
Pre-transition undershoot
Pre-transition overshoot
Waveform epoch
t
IEC
Figure 2 – Overshoot, undershoot, state levels, and state boundaries
for a single positive-going transition
[SOURCE: IEC 60469:2013, 3.2.19, modified – the reference to Figures 5 and 6 in the source
definition has been replaced by the reference to Figure 2.]
3.14
parameter
any value (number multiplied by a unit of measure) that can be calculated from a waveform

– 12 – IEC 62754:2017  IEC 2017
[SOURCE: IEC 60469:2013, 3.2.20]
3.15
maximum peak
pertaining to the greatest value of the waveform
[SOURCE: IEC 60469:2013, 3.2.21]
3.16
minimum peak
pertaining to the least value of the waveform
[SOURCE: IEC 60469:2013, 3.2.22]
3.17
pulse duration
difference between the first and second transition occurrence instants
[SOURCE: IEC 60469:2013, 3.2.27, modified – the note has been deleted.]
3.18
pulse separation
duration between the 50 % reference level instant, unless otherwise specified, of the second
transition of one pulse in a pulse train and that of the first transition of the immediately
following pulse in the same pulse train
[SOURCE: IEC 60469:2013, 3.2.28]
3.19
waveform reconstruction
deconvolution
process of removing the effect of the measurement instrument, connectors, cables, and jitter
on the measured waveform
Note 1 to entry: This process deconvolves the impulse response of the measurement instrument from the
measured waveform.
3.20
sample
element of a sampled waveform, given in units of the amplitude of the signal at a given time
3.21
signal
physical phenomenon, one or more of whose characteristics may vary to represent
information
Note 1 to entry: This phenomenon is a function of time.
[SOURCE: IEC 60469:2013, 3.2.38]
3.22
state
particular level or, when applicable, a particular level and upper and lower limits (the upper
and lower state boundaries) that are referenced to or associated with that level
Note 1 to entry Unless otherwise specified, multiple states are ordered from the most negative level to the most
positive level, and the state levels are not allowed to overlap. The most negative state is called state 1. The most
positive state is called state n. The states are denoted by s , s , …, s ; the state levels are denoted by level(s ),
1 2 n 1
level(s ), …, level(s ); the upper state boundaries are denoted by upper(s ), upper(s ), …, upper(s ); and the lower
2 n 1 2 n
state boundaries are denoted by lower(s ), lower(s ), …, lower(s ).
1 2 n
SEE Figure 2.
[SOURCE: IEC 60469:2013, 3.2.40, modified – the reference to Figure 2 has been added and
note 2 of the original definition has been deleted.]
3.23
state boundaries
upper and lower limits of the states of a waveform
SEE Figure 2.
Note 1 to entry: All values of a waveform that are within the boundaries of a given state are said to be in that
state. The state boundaries are defined by the user.
[SOURCE: IEC 60469:2013, 3.2.41, modified – the reference to Figure 2 has been added.]
3.24
state occurrence
contiguous region of a waveform that is bounded by the upper and lower state boundaries of a
state, and whose duration equals or exceeds the specified minimum duration for state
attainment. The state occurrence consists of the entire portion of the waveform that remains
within the state boundaries of that state.
th
Note 1 to entry State occurrences are numbered as ordered pairs (s ,n), where s refers to the i state, and n is
i i
the number of the occurrence of that particular state within the waveform epoch. In a given waveform epoch, when
the waveform first enters a state s , that state occurrence is (s , 1). If and when the waveform exits that state, that
1 1
state occurrence is over. If and when the waveform next enters and remains in state s , that state occurrence
would be labelled (s , 2); and so on.
[SOURCE: IEC 60469:2013, 3.2.42, modified – the note has been shortened so that it does
not discuss figures that are not contained in this document]
3.25
timebase
that component of a measurement instrument that provides the unique instant for each
sample in a sampled waveform
Note 1 to entry: The timebase provides a vector of sampling instants where each instant corresponds to a unique
sample in the waveform. Often the interval between sample instants is not uniform and exhibits both systematic
and random errors.
3.26
transition
contiguous region of a waveform that connects, either directly or via intervening transients,
two state occurrences that are consecutive in time but are occurrences of different states
[SOURCE: IEC 60469:2013, 3.2.47]
3.26.1
negative-going transition
transition whose terminating state is more negative than its originating state
Note 1 to entry: The endpoints of the negative-going transition are the last exit of the waveform from the higher
state boundary and the first entry of the waveform into the lower state boundary.
[SOURCE: IEC 60469:2013, 3.2.47.1, modified – note 2 has been deleted.]

– 14 – IEC 62754:2017  IEC 2017
3.26.2
positive-going transition
transition whose terminating state is more positive than its originating state
Note 1 to entry: The endpoints of the positive-going transition are the last exit of the waveform from the lower
state boundary and the first entry of the waveform into the higher state boundary.
[SOURCE: IEC 60469, 3.2.47.3, modified – note 2 has been deleted.]
3.27
transition duration
difference between the two reference level instants of the same transition
Note 1 to entry: Unless otherwise specified, the two reference levels are the 10 % and 90 % reference levels.
[SOURCE: IEC 60469:2013, 3.2.48, modified – note 2 has been deleted.]
3.28
transition occurrence instant
first 50 % reference level instant, unless otherwise specified, on the transition of a step-like
waveform
SEE Figure 1.
[SOURCE: IEC 60469:2013, 3.2.13.6, modified – only the reference to Figure 1 has been
kept.]
3.29
transition settling duration
time interval between the 50 % reference level instant, unless otherwise specified, and the
final instant the waveform crosses the state boundary of a specified state in its approach to
that state
[SOURCE: IEC 60469:2013, 3.2.49, modified – the note has been deleted.]
3.30
transition settling error
maximum error between the waveform value and a specified reference level within a user-
specified interval of the waveform epoch. The interval starts at a user-specified instant
relative to the 50 % reference level instant
[SOURCE: IEC 60469:2013, 3.2.50]
3.31
undershoot
waveform aberration within a post-transition aberration region or pre-transition aberration
region that is less than the lower state boundary for the associated state level. If more than one
such waveform aberration exists, the one with the largest magnitude is the undershoot unless
otherwise specified
SEE Figure 2.
[SOURCE: IEC 60469:2013, 3.2.53, modified – the reference to Figures 5 and 6 has been
replaced by the reference to Figure 2.]
3.32
waveform
representation of a signal (for example, a graph, plot, oscilloscope presentation, discrete time
series, equations, or table of values)

Note 1 to entry: Note that the term waveform refers to a measured or otherwise-defined estimate of the physical
phenomenon or signal.
[SOURCE: IEC 60469:2013, 3.2.54]
3.32.1
corrected waveform
sampled waveform that is the result of applying corrections to the measured waveform
3.32.2
impulse-like waveform
waveform that, when convolved with an ideal step, yields a step-like waveform
[SOURCE: IEC 60469:2013, 3.2.54.2]
3.32.3
measured waveform
sampled waveform that is the output of a measurement system before any corrections or
reconstructions are applied
3.32.4
reconstructed waveform
sampled waveform that is the result of applying waveform reconstruction methods to the
corrected waveform
3.32.5
reference waveform
waveform against which other waveforms are compared
[SOURCE: IEC 60469:2013, 3.2.54.3]
3.32.6
sampled waveform representation
waveform which is a series of sampled numerical values taken sequentially or nonsequentially
as a function of time
Note 1 to entry: This will also be called a sampled waveform and the process is called sampling.
[SOURCE: IEC 60469:2013, 3.2.61.2, modified – the original note 1 has been replaced by a
new note 1.]
3.33
waveform aberration
algebraic difference in waveform values between all corresponding instants in time of a
waveform and a reference waveform in a specified waveform epoch
[SOURCE: IEC 60469:2013, 3.2.55]
3.34
waveform delay (advance)
duration between the first transition occurrence instant of two waveforms
[SOURCE: IEC 60469:2013, 3.2.56]

– 16 – IEC 62754:2017  IEC 2017
3.35
waveform epoch
interval to which consideration of a waveform is restricted for a particular calculation,
procedure, or discussion. Except when otherwise specified, the waveform epoch is assumed
to be the span over which the waveform is measured or defined
[SOURCE: IEC 60469:2013 3.2.57]
3.36
waveform measurement process
realization of a method of waveform measurement in terms of specific devices, apparatus,
instruments, auxiliary equipment, conditions, operators, and observers
Note 1 to entry: In this process, a value (a number multiplied by a unit) of measurement is assigned to the
elements of the waveform.
[SOURCE: IEC 60469:2013, 3.2.59]
3.37
waveform recorder
instrument or device for acquiring and subsequently storing a sequence of data corresponding
to the signal being measured
4 Waveform measurement
4.1 General
A signal is the physical event under scrutiny and is to be measured. A waveform is a
representation of that signal and is, for the purposes of this document, the result of a
waveform measurement process. Although a waveform can be presented in different ways,
only a sampled waveform representation of the measured or otherwise estimated signal is
considered. A sampled waveform is discretized in both amplitude and time because of the
digitization performed by the waveform recorder. Time digitization results in presenting the
waveform as a series of discrete waveform samples. Amplitude digitization results in each
waveform sample having a discrete value. The waveform can be of any signal, from an
ultrafast optical pulse to an ultraslow geologic event. The sampled waveform, y[t ], can be
n
represented mathematically as:
N−1
y[t ]= y(t)δ(t− nΔt) (3)
n
∑
n=0
where y(t) is the signal input into the waveform recorder, t is the time, n is the discrete time
index, N is the number of samples in the waveform, ∆t is the discrete time increment, and δ is
the unit impulse function (δ(t= 0)= 1, δ(t≠ 0)= 0) . This formula describes an idealized
situation in which the measurement system response is a unit impulse function, the sampling
intervals are equally spaced, and there is no noise introduced by the measurement system.

Evénement/ Enregistreur de forme
Transducteur Signal Measured waveform
signal p(t)
g(t) d'entrée x(t) d'onde h(t) ⊗ g(t) y(t )
n
Reconstructed waveform Waveform Corrected waveform
Corrections
x'(t ) reconstruction y'(t )
n n
Deconvolve
Estimation of event/signal
transducer
p'(t )
n
IEC
Figure 3 – Creation of measured, corrected, and reconstructed waveforms
and the final estimate of the input signal
The waveform measurement process is shown diagrammatically in Figure 3 and results in the
measured waveform, which has a sampled waveform representation. Subsequent corrections
result in increasingly more accurate estimations of the input signal. This version of the
document, due to the complexity of computing waveform parameter uncertainties, will apply
only to the measured waveform. Corrected waveforms and reconstructed waveforms will be
treated in a subsequent edition, but are discussed briefly in Clause 5.
4.2 Waveform parameters
Waveform parameters are values representing important characteristics of a waveform.
Typically, waveform parameters depict noticeable characteristics of a waveform that facilitate
the discussion, analysis, and comparison of waveforms. These parameters, along with their
definitions, are provided in IEC 60469.
The analysis for computing measurement uncertainties for a given set of waveform
parameters extracted from a measured waveform will be developed. Consequently,
information on the performance requirements relative to a measurement application is
discussed. Measurement uncertainties of corrected waveform parameters will be briefly
discussed in 5.2 and sample-by-sample uncertainties of corrected waveforms in 5.3.2.
Measurement uncerta
...