Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

1.
M.
Chavez
,
M.
Besserve
,
C.
Adam
, and
J.
Martinerie
,
J. Neurosci. Methods
154
,
149
(
2006
).
2.
L.
Xu
,
Z.
Chen
,
K.
Hu
,
H. E.
Stanley
, and
P. C.
Ivanov
,
Phys. Rev. E
73
,
065201(R)
(
2006
).
3.
J.
Sun
,
J.
Zhang
,
J.
Zhou
,
X.
Xu
, and
M.
Small
,
Phys. Rev. E
77
,
046213
(
2008
).
4.
J.
Wang
and
Z.
Liu
,
EPL
102
,
10003
(
2013
).
5.
A. S.
Pikosvsky
,
M. G.
Rosenblum
, and
J.
Kurths
,
Synchronization a Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
2001
). ISBN: 0521592852.
6.
N.
Delprat
,
B.
Escudié
,
P.
Guillemain
,
R.
Kronland-Martinet
,
P.
Tchamitchian
, and
B.
Torrésani
,
IEEE Trans. Inf. Theory
38
,
644
(
1992
).
7.
V. S.
Anishchenko
,
T. E.
Vadivasova
, and
G. I.
Strelkova
,
Fluctuation Noise Lett.
4
,
L219
(
2004
).
8.
R. J.
Barry
,
V.
de Pascalis
,
D.
Hodder
,
A. R.
Clarke
, and
S. J.
Johnstone
,
Int. J. Psichophysiol.
47
,
187
(
2003
).
9.
S. M.
Doesburg
,
J. J.
Green
,
J. J.
McDonald
, and
L. M.
Ward
,
Brain Res.
1303
,
97
(
2009
).
10.
T. I.
Netoff
and
S. J.
Schiff
,
J. Neurosci.
22
,
7297
(
2002
).
11.
A. E.
Hramov
and
A. A.
Koronovskii
,
Chaos
14
,
603
(
2004
).
12.
A. E.
Hramov
,
A. A.
Koronovskii
,
M. A.
Kurovskaya
, and
O. I.
Moskalenko
,
Phys. Rev. E
71
,
056204
(
2005
).
13.
M. G.
Rosenblum
,
A. S.
Pikovsky
, and
J.
Kuhrts
,
Phys. Rev. Lett.
76
,
1804
(
1996
).
14.
M. G.
Rosenblum
,
A. S.
Pikovsky
, and
J.
Kuhrts
,
Phys. Rev. Lett.
78
,
4193
(
1997
).
15.
A. S.
Pikovsky
,
M. G.
Rosenblum
,
V.
Osipov
, and
J.
Kurths
,
Physica D
104
,
219
(
1997
).
16.
U.
Parlitz
,
L.
Junge
,
W.
Lauterborn
, and
L.
Kocarev
,
Phys. Rev. E
54
,
2115
(
1996
).
17.
D.
Maza
,
A.
Vallone
,
H.
Mancini
, and
S.
Boccaletti
,
Phys. Rev. Lett.
85
,
5567
(
2000
).
18.
C. M.
Ticos
, Jr.
,
W. B.
Pardo
,
J. A.
Walkenstein
, and
M.
Monti
,
Phys. Rev. Lett.
85
,
2929
(
2000
).
19.
D. Y.
Tang
,
R.
Dykstra
,
M. W.
Hamilton
, and
N. R.
Heckenberg
,
Phys. Rev. E
57
,
3649
(
1998
).
20.
Y.
Aviad
,
I.
Reidler
,
W.
Kinzel
,
I.
Kanter
, and
M.
Rosenbluh
,
Phys. Rev. E
78
,
025204(R)
(
2008
).
21.
D. J.
DeShazer
,
R.
Breban
,
E.
Ott
, and
R.
Roy
,
Phys. Rev. Lett.
87
,
044101
(
2001
).
22.
P.
Tass
,
M. G.
Rosenblum
,
J.
Weule
,
J.
Kurths
,
A.
Pikovsky
,
J.
Volkmann
,
A.
Schnitzler
, and
H. J.
Freund
,
Phys. Rev. Lett.
81
,
3291
(
1998
).
23.
F.
Mormann
,
T.
Kreuz
,
R. G.
Andrzejak
,
P.
David
,
K.
Lehnertz
, and
C. E.
Elger
,
Epilepsy Res.
53
,
173
(
2003
).
24.
K.
Jerger
,
S. L.
Weinstein
,
T.
Sauer
, and
S. J.
Schiff
,
Clin. Neurophysiol.
116
,
545
(
2005
).
25.
M. G.
Rosenblum
,
A. S.
Poikovsky
, and
J.
Kurths
,
Fluctuations Noise Lett.
4
,
L53
(
2004
).
26.
J. P.
Pijn
,
J.
van Neerden
,
A.
Nost
, and
F. H.
Lopes da Silva
,
Electroencephalogr. Clin. Neurophysiol.
79
,
371
(
1991
);
[PubMed]
J. P.
Pijn
,
D. N.
Velis
,
M. J.
van der Heide
 et al,
Brain Topogr.
9
,
249
(
1997
).
[PubMed]
27.
M.
Casdagli
,
J. R. Stat. Soc. B
54
,
303
(
1991
).
28.
29.
J.
Theiler
and
P. E.
Rapp
,
Electroencephalogr. Clin. Neurophysiol.
98
,
213
(
1996
).
31.
R. A.
Stepien
,
Acta Neurobiol.
62
,
277
(
2002
).
32.
R. G.
Andrzejak
,
K.
Schindler
, and
C.
Rummel
,
Phys. Rev. E
86
,
046206
(
2012
).
33.
C.
Rummel
,
E.
Abela
,
M.
Müller
 et al,
Phys. Rev. E
83
,
066215
(
2011
).
34.
F.
Mormann
,
T.
Kreuz
, and
C.
Rieke
,
Clin. Neurophysiol.
116
,
569
(
2005
).
35.
D.
Gosh
,
EJTP
6
,
125
(
2009
).
36.
B.
Picinbono
,
IEEE Trans. Signal Process.
45
,
552
(
1997
).
37.
T.
Pereira
,
M. S.
Baptista
, and
J.
Kurths
,
Phys. Lett. A
362
,
159
(
2007
).
38.
L.
Cohen
,
P.
Loughlin
, and
D.
Vakman
,
Signal Process.
79
,
301
(
1999
).
39.
W.
Nho
and
P. J.
Loughlin
,
IEEE Sig. Proc. Lett.
6
,
78
(
1999
).
40.
B.
Boashash
,
Proc. IEEE
80
,
520
(
1992
).
41.
L.
Mandel
,
Am. J. Phys.
42
,
840
(
1974
).
42.
P. J.
Loughlin
and
B.
Tacer
,
IEEE Signal Process. Lett.
4
,
123
(
1997
).
43.
P. M.
Oliveira
,
IEEE Signal Process. Lett.
6
,
81
(
1999
).
44.
F.
Mormann
,
K.
Lehnertz
,
P.
David
, and
C. E.
Elger
,
Physica D
144
,
358
(
2000
).
45.
S.
Pocket
,
G. E. J.
Bold
, and
W. J.
Freeman
,
Clin. Neurophysiol.
120
,
695
(
2009
).
46.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
, 2nd ed. (
Cambridge University Press
,
Cambridge, England
,
2003
).
47.
D.
Gabor
,
J. Inst. Electr. Eng.
93
,
429
(
1946
).
48.
J.
Oswald
,
IRE Trans. Circuits Syst.
3
,
244
(
1956
).
49.
50.
B.
Picinbono
, in
Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
(
1998
), p.
293
.
51.
52.
L. B.
White
and
B.
Boashash
,
IEEE Trans. Inf. Theory
36
,
830
(
1990
).
53.
G.
Nolte
,
O. B.
Lewis Wheaton
,
Z.
Mari
,
S.
Vorbach
, and
M.
Hallett
,
Clin. Neurophysiol.
115
,
2292
(
2004
).
54.
M.
Vinck
,
R.
Oostenveld
,
M.
van Wingerden
,
F.
Battaglia
, and
C. M. A.
Pennartz
,
Neuroimage
55
,
1548
(
2011
).
55.
M.
Müller
,
G.
Baier
,
A.
Galka
,
U.
Stephani
, and
H.
Muhle
,
Phys. Rev. E
71
,
046116
(
2005
).
56.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in Fortran
, 2nd ed., The Art of Scientific Computing (
Cambridge University Press
,
1999
).
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