SINGLE-ENDED LINE TESTING - A WHITE BOX APPROACH
Patrick Boets and Leo Van Biesen
Department of Fundamental Electricity
and Instrumentation,
Vrije Universiteit Brussel,
Pleinlaan 2,
B-1050 Brussels, Belgium,
pboets@vub.ac.be
Tom Bostoen
Department of Research
and Innovation,
ALCATELL,
F. Wellesplein 1
B-2018 Antwerp,Belgium,
tom.bostoen@alcatel.be
ABSTRACT
A measurement, modelling and identification system is
proposed to qualify a subscriber line with the constraint
that only measurements can be conducted at the Central
Office. The system uses the one-port scattering parameter as a base measurement of the loop. The time domain
version of this scattering parameter will be pre-processed
so that the features, which are the start, maximum and end
positions of a reflection, are clearly visible and hence detectable. These features are used by the interpreting expert
system which performs a topology estimation of that loop.
Once the topology is known, a loop model, based on the
physical properties of a twisted pair line, is build and the
loop can be identified using a Maximum Likelihood Estimator. Next, the end-to-end transfer function will be calculated. The results and observations of a measurement campaign using a France Telecom cable plant will illustrate the
proposed Single-Ended Line Testing approach.
In this paper, a well-founded model based approach
for SELT is given. For the moment, it operates under
the following constraints: i. It is assumed that the load
impedance is high enough to be considered as an open line
end. Most terminals such as telephone, fax and minitel
have a high impedance but some electronic POTS systems
and ADSL-modems are better matched to the line. ii. The
CP location is known in case bridged taps exist in the network. iii. a priori knowledge about the cable properties
must be available. iv. Cable faults must be removed before
applying SELT, because faults are not yet included in the
models.
The noise level identification at the CP side is not
treated in this paper but the authors refer to [2, 5]
2
2.1
KEY WORDS
Channel Estimation, System Capacity Analysis
1
Description of the approach
Measurement Quantities at CO
In order to determine the channel capacity of the Device
Under Test (DUT), two loop properties have to be identified. Firstly, the end-to-end Power Transfer Function
(PTF) in a predefined termination impedance, e.g. 100Ω
for ADSL. Secondly, the Power Spectral Density (PSD) at
the receiver must be measured or predicted.
An estimation of the PTF should be obtained from a
testhead independent quantity. This quantity must contain
fundamental information about the loop but may not depend on the nature of the excitation signal - if one uses plain
Time Domain Reflectometry (TDR) then the trace depends
on the shape of the injected pulse too. Possible information
carrying quantities are: the one-port scattering parameter
S11 (ω) or the input impedance Zin (ω) of the loop. The
quantities are mostly represented in the frequency domain
but their time domain versions are valid descriptions too.
The one-port scattering parameter S11 (ω) was chosen
for the description of the loop’s behavior and is defined as
(see also figure 1):
¯
b(ω) ¯¯
S11 (ω) =
(1)
a(ω) ¯Zbase
Introduction
Operators today are performing loop qualification to provide, support and troubleshoot xDSL service. Up till now
line testing happened by placing measurement equipment
at the Central Office (CO) and the Customer Premises (CP)
side. This requires an expensive truck roll at the CP location but the measurement is quite accurate. Recently,
Single-Ended Line Testing (SELT) has become an new and
interesting topic [1, 2, 3, 4, 5, 6, 7]. The idea is to perform
measurements at the Central Office only in order to obtain
a reasonable estimate of the line quality. Therefore, the objectives of SELT are the prediction of the end-to-end transfer function of the loop, the knowledge of the loop topology
(topography, line types and line lengths), the identification
of the disturbers at the receiver and even cable fault detection is possible. Once the channel topology and disturbers
are known, the capacity in bits/s (e.g. for ADSL or VDSL)
can be predicted. SELT measurements can be performed
by stand-alone equipment but it is commercially more interesting by letting the broadband modem itself do the tests.
422-039
Daniel Gardan
Department of R&D/RTA Caractérisation
du Réseau Cuivre,
France Telecom,
Avenue Pierre Marzin 2,
22307 Lannion Cedex - France,
daniel.gardan@rd.francetelecom.com
with a(ω) the incident voltage wave and b(ω) the reflected
voltage wave both given in the base impedance Zbase and
393
a
Zg
E
+
-
4000
I1
s11(t) 100Ω
s11(t) quasi−optimal
s11(t) optimal
3500
ZL
Loop
V1
3000
2500
2000
b
1500
Figure 1. The input port of a subscriber line and the corresponding electrical quantities.
1000
500
0
0
20
40
60
80
100
120
140
time (us)
S11 (ω) is related with the input impedance according to:
Zin (ω) =
V1 (ω)
1 + S11 (ω)
= Zbase
I1 (ω)
1 − S11 (ω)
Figure 2. The impulse response of a 4km long 0,4mm
polyethylene cable shown in different bases.
(2)
To stimulate the DUT, multi-tone signals are chosen
as excitation signals for a number of reasons: 1. The measurement method should be able to be implemented on
a Discrete Multi-Tone (DMT) modem, such as ADSL or
VDSL. 2. The measurements take place on the networks
of the operators. It is important that the power spectral
density masks, as proposed by the standards, are not violated. 3. The measurement time can be strongly reduced
because multi-tone signals probe the DUT over the complete frequency band. E.g. one ADSL DMT symbol can
test the loop from 4.3125kHz up to 1.104MHz in about
232µs. This leaves enough room for a huge number of
averages to be used for noise reduction purposes without
making this measurement inherently slow.
For the moment, S11 (ω) measurements are conducted
after calibrating the analog front-end of the DMT modem.
Basically, three S11 (ω) measurements are necessary to calculate a calibration data set and a very common choice is to
use an open-ended, short-circuited and a loaded measurement port. Using these three measurements, a set of three
frequency dependent coefficients can be calculated that allow the calibration correction of the the raw S11 (ω) measurement. In general, the linear distortion caused by the
fixed front-end - the test leads and the test bus between the
testhead and the DUT may be included too - can be removed.
Measurement of the PSD at the measurement port
is rather straightforward and does not require complicated
calibration techniques. A table lookup method method allows for the compensation of the frequency response function from the input to the analog to digital converter.
2.2
as if the impulse response was obtained by an ideal measurement instrument matched to the line and placed at the
calibration plane. In the second place, it will provide an estimate of the arrival time of the first significant reflection.
In order to produce the deliverables, the preprocessor
will tackle four problems:
1. The base impedance Zbase of the calibrated S11 (ω)
is not suited for the visualization of s11 (t). The ideal
base impedance is the characteristic impedance Zc (ω) of
the first line segment of the loop. Identifying the input
impedance of the loop with the characteristic impedance
of a transmission line using the physical VUB-model
[1, 9, 11] will be a sufficient approximation of the ideal
base impedance. A simulation example is given in figure 2.
It can be seen that the estimated base approaches very close
the ideal base impedance. The advantage of using a parametric model is that no a priori knowledge is necessary of
that first line segment. Existing methods [4] use a measured
curve from a database of Zc (ω) curves but, the behavior of
the characteristic impedance depends also on external influences such as temperature and aging. And last but not
least, the properties of a twisted pair vary from pair to pair
in the same cable due to the different twist rates used [10].
Therefore, a model based approach is more flexible to deal
with these unforeseen impedance deviations.
2. The second action is the reduction of the oscillations in s11 (t) when applying the inverse Discrete Fourier
Transform (iDFT) on the calibrated version of S11 (ω).
Power regulations do not allow DC injection and high frequency excitation is regulated (E.g. ADSL regulations limit
excitation above 1,104MHz) and even unnecessary due to
the extremely high cable attenuation. So, a number of spectral lines (tones) of the excitation signal will not contain
any imposed power and S11 (ω) is unpredictable at those
spectral lines. Zeros substitution solves the problem but
the frequency contents of S11 (ω) is windowed now. Application of an iDFT will cause oscillations in s11 (t) but
these can be removed by applying a filter on S11 (ω) or by
Pre-Processing
The pre-processing will transform the obtained scattering
parameter S11 (ω) into its time domain counterpart s11 (t)
also called the impulse response of the DUT [10]. The preprocessor deliverables are in the first place to calculate a
calibrated version of the impulse response. It is exactly
394
using a convolution of s11 (t) with a specialized function.
Valid candidates are linear phase FIR filters and the Gauss
function respectively.
3. The duration of the time window depends on the
used tone spacing. This amounts to 232µs for DMT based
test heads such as ADSL and VDSL. In most cases, the impulse response duration of the DUT is much longer than
that so time aliasing will occur. It is also a task of the preprocessor to remove this time-alias from s11 (t). The time
aliasing is clearly visible in figure 4 because the curves do
not contain a flat baseline. The time-alias on s11 (t) can
be sufficiently removed by fitting an exponential decaying
function Ae−Bt on the last portion of the tail of the timealiased curve and next by subtracting the predicted alias
from the aliased curve.
4. The last task of the preprocessor concerns the estimation of the duration of a neutral zone T0 which does
not contain meaningful reflections as caused by cable junctions and line extremities. As shown before in figure 4,
all reflections prior to 10µs are not related with real cable
junctions but with connectors and local impedance nonhomogeneities of the cable. The knowledge of T0 will
prevent the topology classification from using such false
reflections. Two mechanisms are used to estimate T0 : i.
Use of the equal-level impulse response s11,el (t); ii. The
use of thresholds on s11,el (t). The equal-level impulse response s11,el (t) is obtained by multiplying the de-aliased
impulse response with a time varying amplification factor
λα (t). This factor is based on the magnitude behavior of
the impulse response of a generic transmission line. If the
time increases, the λ(t) increases as well so that the maximum of the impulse response of that generic line multiplied with λ(t) remains constant whatever the line length
amounts to. In practice a relaxation factor α was foreseen
for shorter loops because their reflections are in any case
strong enough to reach above the irregular reflections. The
preceding detection of shorter loops is possible when one
looks at the amount of normalized reflected power or when
the Root Mean Squares Error, which is obtained from approximating the input impedance of the loop with the physical model (see item 1), is large. A simple threshold mechanism applied on s11,el (t) is used to obtain T0 .
2.3
other which complicates the feature detection of each individual reflection. There exist some methods to separate
reflections from each other, but none of them is suited for a
separate loop identification because most existing methods
[4, 13] use an embedded feature extraction, topology classification and identification method in contrast to our sequential approach. The iterative peak detection algorithm can
be split up in three subparts: a. The extrema and inflection
points of s11 (t) are detected; b. A numerical prediction of
the tail of the first peak is made using a mathematical function; c. The overlapping part of the peak under study will
be replaced with the in section b estimated continuation of
that peak. A residual response can be calculated whereafter
steps a, b and c can be repeated with this residual response.
The iteration stops when the energy of the residue signal is
below a predefined level.
2. Secondly, when the features of s11 (t) are known,
a preliminary topology prediction is given using a probabilistic reasoning system. The supported topologies are
(L, LL, LLL, LT L, LT T L, LT LT L)
(3)
with L an inline segment and T a tap. This system, which
is called a belief network, uses Baye’s rule as the basic reasoning principle. So, the most likely topology T given the
fact that one knows the features of the peaks F is obtained
as follows:
P (T |F ) =
P (F |T ) · P (T )
P (F )
(4)
The knowledge base P (F |T ) is inferred, by solving an optimization problem, from a user selected set of rules, e.g.
P (positive first peak|second line segment not present) = 0.9
(5)
Unconditional rules or facts also exists, e.g. if an operator does not have bridged taps in its access network then
P (loops with taps) = 0. Two belief networks were designed. The first reasons on the signs of the peaks and the
seconds one uses the positions of the peaks. A weighted average on the outcome of both networks produces the final
topology estimation.
3. Thirdly, a Rule Based System (RBS) tries to interpret the previous topology prediction. It will provide the
most logic topology with the corresponding values for the
delays and line types of each line segment of the loop. In
order to guarantee a valid result, a priori information about
the cable network is used as much as possible. Important a
priori information are the existence of taps in a network, the
wire gauge order in cascaded networks, the line types used
in the network etc. The RBS system is deterministic, because it is build on an elaborated set of deterministic rules.
In the beginning, the RBS reasons on features and gradually it adds more physical reality until an s11 (t) curve is
simulated for comparison with the real measured one. If an
error is found then the solution will be improved or it will
create of a new solution.
Topology Classification
As soon as the preprocessor delivers a de-aliased version
of the impulse response s11 (t) and the accompanying estimation of the neutral zone T0 , a topology classification of
the loop can take place. The goal of the classification is the
provisioning of the frequency domain physical model of
S11 (ω) and the corresponding starting values to be used in
the loop identification procedure. The classification takes
place in three phases and will be briefly outlined (a detailed
discussion is found in [3]).
1. Firstly, the features of s11 (t) are detected. Important features are the start, maximum and end position of
an observed reflection. In practice reflections overlap each
395
2.4
Loop Identification
1500
1000
The last important phase comprises the identification of the
calibrated measurement S11 (ω) with a parametric model
S11,m (ω, P), which is based on transmission line theory
and twisted pair modelling. It is possible to construct such
a model because the topology together with a set of initial
values of the parameters P, which have been previously determined, are available. An S11 (ω) Maximum Likelihood
Estimator (MLE) [12] was constructed for the parameter
identification (an in-dept description is found in [1]).
The S11 (ω) estimator uses the VUB cable model
[1, 9, 11]. This model is based on the geometric and the
material properties of a 2-wire line. The model covers the
skin-effect and the proximity effect in the behavior of the
series-impedance of the (copper) conductors. The dielectric modelling is kept very simple because most lines use
polyethylene as an insulation material. A Popular model
such as the BT-model (British Telecom) [8] is not utilized,
due to it’s unsound mathematical construction.
The MLE was constructed using an output error
model and this involves that the following cost function C
needs to be minimized:
C=
N
2
X
|S11 (ωk ) − S11,m (ωk , P)|
k=1
σ 2 (ωk )
σ 2 (ωk ) ⊗ |W (ωk )|
s11 [dimensionless]
−500
−1000
−1500
−2000
−2500
−3000
0
5
10
15
20
25
length [km]
Figure 3. The detected features of an LLL-loop (1200m1200m-2400m).
3 Measurement Results
A measurement campaign was conducted on the cable plant
of the R&D department of France Telecom (FT). Only
loops which contain a cascade of line sections were selected, because the access network of FT does not has any
taps. Moreover, the loops start at the CO with thin 0,4mm
wires and as more sections are added the wire diameter increases. This information together with the knowledge of
the frequency domain cable functions of each cable type,
are used as a priori knowledge. Before the actual measurements are carried out, cable calibration data was collected. The propagation function γ(ω) and the characteristic impedance Zc (ω) of each possible cable type used in the
network were measured. In fact, each pair in a cable bundle has slightly different characteristics. Therefore, an averaged value was taken over a few characteristic line pairs
of that cable bundle. Three cable types were used in the
test: a 0,4mm, 0,6mm and 0,8mm FT polyethylene insulated shielded twisted pair cable.
An individual example illustrates the previously described processes. It represents an LLL-topology where
a section of 1,2km 0,4mm cable is successively cascaded
with a 1,2km long 0,6mm cable and a 2,4km long 0,8mm
cable. The total loop length amounts to 4,8km. Figure 4
shows the aliased impulse respons s11 (t) in the estimated
base impedance and the de-aliased impulse response. As
one can see, de-aliasing is extremely necessarily especially
when an equal level impulse response has to be derived
from the former. The neutral zone T0 has been estimated
using a threshold level on s11,el (t) and its value is close
enough to the real delay of the first meaningful reflection
(see figure 5). The value of T0 has not been affected by
the irregular reflections which are present in the beginning
of s11 (t). The feature extraction results are depicted in figure 3. Three significant reflections are found. Starting from
an uniform distribution, the belief network infers an LLLtopology with a probability of 57% (18% for an LL- and
(6)
N
2
X
|S11 (ωk ) ⊗ W (ωk ) − S11,m (ωk , P) ⊗ W (ωk )|
k=1
Peak Start
Peak Extremum
Peak End
0
with σ 2 (ωk ) the variance of the measured S11 (ω) at the angular frequency ωk . For loops longer than 2km, impedance
irregularities coming from the local non-homogeneities and
connectors disturb S11 (ω) in the complete frequency band.
These disturbing effects are removed by using a time window on s11 (t) and hence S11 (ω) needs to be convolved
with the Fourier transform W (ω) of that window. In this
case the cost function becomes:
C=
s11(t)
500
2
(7)
A Levenberg-Marquardt cost function minimizer is used.
It combines the Gauss-Newton and gradient-descent procedures in a intelligent way [12].
2.5 Channel Capacity Prediction
Knowing the loop topology is of great importance for an
operator to test, pre-qualify, debug and maintain a loop [7].
If the PSD of the noise at the receiver side is known, using
a direct measurement or an estimation of the PSD, then in
addition a bitrate prediction is possible. In order to obtain
the theoretical channel capacity, Shannon’s capacity formula can be used. If a bitrate prediction is required that is
connected with the used modem technology such as ADSL
or VDSL, then one has to take the filtering, bit-loading,
ADC-resolution, used tones etc. into account. For some
non-standardized parts of a modem particular information
is required from the manufacturer.
396
5000
500
4000
0
measurement
model
initial model
3000
−500
2000
−1000
s11
s11(t)
1000
−1500
0
Time Aliased s11
Time Alias
Fit interval
De−Aliased s11
−1000
−2000
−2000
−2500
−3000
−3000
−4000
0
50
100
150
200
20
250
30
40
50
60
Time [µs]
70
t [µs]
80
90
100
110
120
Figure 6. The approximation of the measurement s11 (t)
(dots) with the model (solid). The identification starts with
the initial model(dash) as produced by the RBS.
Figure 4. The time aliased and de-aliased impulse response
of an LLL-loop.
−3
8
x 10
Loop Power Transfer Fuction
-20
6
Predicted
Exact
-30
Delay = 10.8µs
4
[dB] -40
-50
2
s11,el(t)
-60
0
-70
0
50
100
150
200
250
f [kHz]
300
350
400
450
500
−2
-0.1
Error
−4
-0.2
−6
[dB]
-0.3
−8
−10
-0.4
-0.5
0
50
100
150
200
250
time [µs]
0
50
100
150
200
250
f [kHz]
300
350
400
450
500
Figure 5. The equal level impulse response of an LLL-loop.
The first line segment is 1200m long.
Figure 7. The measured and the predicted Power Transfer
Function of the LLL-loop (1200m-1200m-2400m).
25% for an L-topology) and the RBS was able to explain
all the detected features that are connected with this LLLtopology. The loop identification needed about 13 iterations to minimize the cost function (7). The time domain
result is shown in figure 6. The approximation of the s11 (t)
measurement with the model is very good. Modelling errors still exist, but this is explained by the individual pair
difference with respect to the averaged cable calibration
data. This difference will always be present because the
pairs in a cable are not exactly the same. Finally a comparison was made between the measured end-to-end power
transfer function and the predicted one. The deviation is
below 0,5dB in a frequency band from 4kHz-500kHz.
More topology configurations were tried out and the
results are given in table 1. The symbols indicated with ’ˆ’
represent the estimates and BR means the downstream bi-
trate of the channel when a flat noise level of -130dBm/Hz
is used. The bitrate is obtained using a frequency band from
138kHz (tone No. 32) up to 500kHz (tone No. 115). The
amount of transmitted information bits above 500kHz is
rather limited, so in this high frequency region no power
transfer function measurements were carried out. Inspection of table 1 shows that the overall performance is very
good. L- and LL-loops can be identified without problems.
For LLL-loops, the length of the first line segment is of
overriding importance for the correct topology prediction.
This is caused by the high attenuation and dispersion of the
0,4mm cable. It really smears out and covers all reflection
information in s11 (t). However, even when missing the
correct topology, the systems still succeeds in providing a
reasonable estimate of the total loop length and bitrate prediction.
397
[3] T. Vermeiren, T. Bostoen, F. Louage, P. Boets and X.
O. Chehab, ”Subscriber Loop Topology Classification
by means of Time Domain Reflectometry”, IEEE International Conference on Communications, Anchorage
USA, 11-15 May, 2003
Table 1. Measurement results obtained from the France
Telecom cable plant.
topo
L
L
L
L
L
LL
LL
LL
LL
LL
LL
LL
LL
LL
LL
LLL
LLL
LLL
LLL
LLL
LLL
LLL
LLL
LLL
LLL
4
L1
L̂1
L2
L̂2
L3
L̂3
Ltot
L̂tot
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
Ltot
error
[%]
BR
error
[%]
600
1200
2400
3600
4800
300
300
1200
1200
1200
2400
2400
2400
2400
2400
600
600
1200
1200
1200
1200
2400
2400
3600
3600
608
1212
2404
3583
4761
297
235
1191
1203
1164
2344
2368
2378
2389
2403
598
600
1200
1203
1200
1203
2366
2333
3538
-
1259
1281
1299
2437
1316
2435
-
600
1200
2400
3600
4800
1500
2700
2400
3600
1500
2700
3000
3600
4800
6000
2100
2400
3000
4200
3600
4800
4800
4200
5400
6000
608
1212
2404
3583
4761
1506
2716
2413
3581
1518
2711
2998
3591
4766
5909
2112
2410
3008
4183
3594
4760
4738
4156
5340
-
1,3
1,0
0,2
-0,5
-0,8
0,4
0,6
0,5
-0,5
1,2
0,4
-0,1
-0,3
-0,7
-1,5
0,6
0,4
0,3
-0,4
-0,2
-0,8
-1,3
-1,0
-1,1
-
0.05
0.25
0.5
1.5
5.3
0.3
0.8
0.6
0.95
0,0
0.21
0.24
0.15
0.5
3,3
0.8
0.9
1.4
2.7
0.5
1.3
15,0
12,0
17,0
-
1200
2400
1200
2400
300
300
600
1200
2400
3600
300
600
600
600
1200
1200
1200
600
600
1200
1209
2481
1222
2378
354
367
630
1213
2377
3506
255
529
509
543
1078
1122
2372
1823
1802
-
1200
1200
1200
2400
1200
2400
1200
1200
1200
1200
[4] S. Galli and D.L. Waring, ”Loop Makeup Identification Via Single Ended Testing: Beyond Mere Loop
Qualification”, IEEE Journal of Selected Areas in
Communication-Twisted Pair Transmission, Vol. 20,
No. 5, june 2002, pp923-935
[5] S. Galli, C. Valenti, K. Kerpez, ”A Frequency-Domain
Approach to Crosstalk Identification in DSL Systems”
, IEEE Journal on Selected Areas in Communications,
Special Issue on Multiuser Detection Techniques with
Application to Wired and Wireless Communications
Systems (Part I), vol.19, no.8, August 2001.
[6] D.L. Waring, S. Galli, K. Kerpez and C.F. Valenti
, ”Analysis Techniques for Loop Qualification and
Spectrum Managment”, International Wire and Cable
Symposium, IWCS2000, Atlantic City, USA, 13-16
Nov., 2000
Conclusion
A white box model based approach for single-ended line
testing is proposed. The model is based on a parametric
physical line model to fully describe a line segment and
transmission line theory to make up a frequency domain
model of the one-port scattering parameter of the complete
loop. Single-ended line measurements using discrete multi
tones are pre-processed and produce a calibrated version of
the impulse response of the loop. It was demonstrated that
the visualization in an estimated base impedance reveals
the reflection information, even if the loops are a few km
long. The loop is identified in the frequency domain and the
geometric topology and corresponding initial parameters
values of each line segment is provided by a deterministic
rule based system. The proposed approach is demonstrated
using lab measurements carried out on cables as used in the
access network of France Telecom. Good topology predictions have been obtained for cascaded networks.
[7] P. Melsa and K. Jacobsen , ”Single-Ended Loop Testing (SELT) Expectations and Realities”, march 2003,
http://www.dslprime.com/a/SELTWhitePaperTI.pdf
[8] ANSI T1.413 Issue2 1998, Asymmetric Digital Subscriber Line (ADSL) Metallic Interface
[9] P. Boets, ”Frequency Identification of Transmission
Lines from Time Domain Measurements”, Ph.D. Thesis, june 1997, Free University of Brussels, Brussels,
Belgium
[10] P. Boets, T. Bostoen, L. Van Biesen and T. Pollet,
Measurement, ”Calibration and Pre-Processing of Signals for Single-Ended Subscriber Line Identification”,
IEEE Instrumentation and Measurement Technology
Conference, Vail, Colorado, USA, 20-22 May, 2003
[11] P. Boets, M. Zekri, L. Van Biesen, ”On the Identification of Cables for Metallic Acces Networks”, IEEE
Instrumentation and Measurement Technology Conference, Budapest, Hungary, 21-23 May, 2001
References
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and D. Rabijns, ”Estimation of the Transfer Function
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