System spectral analysis of the fractal ultra-wideband signals
The theoretical basis and practical peculiarities of the system spectral analysis are briefly considered. The necessity and the expediency of simultaneously application of different linear and non-linear integral transforms during the system spectral analysis performance are explained. The system sp...
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| Zitieren: | System spectral analysis of the fractal ultra-wideband signals / L.F. Chernogor, S.G. Kravchenko, O.V. Lazorenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 244-247. — Бібліогр.: 5 назв. — англ. |
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Chernogor, L.F. Kravchenko, S.G. Lazorenko, O.V. 2017-01-18T19:48:21Z 2017-01-18T19:48:21Z 2015 System spectral analysis of the fractal ultra-wideband signals / L.F. Chernogor, S.G. Kravchenko, O.V. Lazorenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 244-247. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 07.50.Qx, 02.30.Uu https://nasplib.isofts.kiev.ua/handle/123456789/112224 The theoretical basis and practical peculiarities of the system spectral analysis are briefly considered. The necessity and the expediency of simultaneously application of different linear and non-linear integral transforms during the system spectral analysis performance are explained. The system spectral analysis usage for investigations of the time-frequency structure of the fractal ultra-wideband signals is shown to be effective and useful. Стисло розглянуто теоретичні засади та практичні особливості системного спектрального аналізу. Роз’яснено необхідність і доцільність одночасного використання різних лінійних і нелінійних інтегральних перетворень для проведення системного спектрального аналізу. Продемонстровано, що застосування системного спектрального аналізу для дослідження часо-частотної структури фрактальних надширокосмугових сигналів є корисним та ефективним. Кратко рассмотрены теоретические основы и практические особенности системного спектрального анализа. Разъяснена необходимость и целесообразность одновременного применения различных линейных и нелинейных интегральных преобразований для проведения системного спектрального анализа. Показано, что использование системного спектрального анализа для исследования время-частотной структуры фрактальных сверхширокополосных сигналов является полезным и эффективным. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нелинейные процессы в плазменных средах System spectral analysis of the fractal ultra-wideband signals Системний спектральний аналіз фрактальних надширокосмугових сигналів Системный спектральный анализ фрактальных сверхширокополосных сигналов Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
System spectral analysis of the fractal ultra-wideband signals |
| spellingShingle |
System spectral analysis of the fractal ultra-wideband signals Chernogor, L.F. Kravchenko, S.G. Lazorenko, O.V. Нелинейные процессы в плазменных средах |
| title_short |
System spectral analysis of the fractal ultra-wideband signals |
| title_full |
System spectral analysis of the fractal ultra-wideband signals |
| title_fullStr |
System spectral analysis of the fractal ultra-wideband signals |
| title_full_unstemmed |
System spectral analysis of the fractal ultra-wideband signals |
| title_sort |
system spectral analysis of the fractal ultra-wideband signals |
| author |
Chernogor, L.F. Kravchenko, S.G. Lazorenko, O.V. |
| author_facet |
Chernogor, L.F. Kravchenko, S.G. Lazorenko, O.V. |
| topic |
Нелинейные процессы в плазменных средах |
| topic_facet |
Нелинейные процессы в плазменных средах |
| publishDate |
2015 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Системний спектральний аналіз фрактальних надширокосмугових сигналів Системный спектральный анализ фрактальных сверхширокополосных сигналов |
| description |
The theoretical basis and practical peculiarities of the system spectral analysis are briefly considered. The necessity and the expediency of simultaneously application of different linear and non-linear integral transforms during the system spectral analysis performance are explained. The system spectral analysis usage for investigations of the time-frequency structure of the fractal ultra-wideband signals is shown to be effective and useful.
Стисло розглянуто теоретичні засади та практичні особливості системного спектрального аналізу. Роз’яснено необхідність і доцільність одночасного використання різних лінійних і нелінійних інтегральних перетворень для проведення системного спектрального аналізу. Продемонстровано, що застосування системного спектрального аналізу для дослідження часо-частотної структури фрактальних надширокосмугових сигналів є корисним та ефективним.
Кратко рассмотрены теоретические основы и практические особенности системного спектрального анализа. Разъяснена необходимость и целесообразность одновременного применения различных линейных и нелинейных интегральных преобразований для проведения системного спектрального анализа. Показано, что использование системного спектрального анализа для исследования время-частотной структуры фрактальных сверхширокополосных сигналов является полезным и эффективным.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112224 |
| citation_txt |
System spectral analysis of the fractal ultra-wideband signals / L.F. Chernogor, S.G. Kravchenko, O.V. Lazorenko // Вопросы атомной науки и техники. — 2015. — № 4. — С. 244-247. — Бібліогр.: 5 назв. — англ. |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №4(98) 244
SYSTEM SPECTRAL ANALYSIS
OF THE FRACTAL ULTRA-WIDEBAND SIGNALS
L.F. Chernogor1, S.G. Kravchenko2, O.V. Lazorenko2
1V.N. Karazin Kharkiv National University, Kharkov, Ukraine;
2Kharkiv National University of Radio Electronics, Kharkov, Ukraine;
E-mail: Leonid.F.Chernogor@univer.kharkov.ua;
1gisone@gmail.com; Oleg-Lazorenko@yandex.ua
The theoretical basis and practical peculiarities of the system spectral analysis are briefly considered. The neces-
sity and the expediency of simultaneously application of different linear and non-linear integral transforms during
the system spectral analysis performance are explained. The system spectral analysis usage for investigations of the
time-frequency structure of the fractal ultra-wideband signals is shown to be effective and useful.
PACS: 07.50.Qx, 02.30.Uu
INTRODUCTION
Last years the new types of the ultra-wideband
(UWB) signals have been proposed. In particular, the
fractal, the random, the direct-chaotic UWB signals, the
UWB signals with changing mean frequency can be
considered as the suitable examples of such new UWB
signal types [1]. These new UWB signal types have
been started to apply in many branches of science and
engineering. Moreover, many natural and artificial pro-
cesses in nature, in particular, in the complex open dy-
namical non-linear system called as the Earth-
atmosphere-ionosphere-magnetosphere were appeared
to be just the UWB processes, which can be classified
as one of those new types [2].
The time-frequency structure of such UWB signals
and processes is appeared to be more complex and mis-
cellaneous than one of the traditional ultra-short UWB
signals was. Therefore, for successful analysis and in-
vestigations of such signals and processes it is necessary
to use, of course, a new analysis method.
One of the possible ways is the application of system
spectral analysis. Actuality of this work is conditioned
to these.
1. FRACTAL ULTRA-WIDEBAND SIGNAL
MODELS
By the definition, a fractal UWB (FUWB) signal is a
UWB signal with self-affine property and fractal dimen-
sion [1, 3].
Many different FUWB signal models as analytical,
as numerical were proposed [1, 3]. In this paper, as an
example, we consider the following model based on the
Weierstrass function:
2 4
2
0
2 4 1
( ) 1
cos 2
;
1
D
M
D n n
n
n
D M
FUWB t b
b sb t
b
where t is the time variable, b is the time scale param-
eter, s is the frequency scale parameter, D is the frac-
tal dimension of the signal, 1 2D , n is the
phase distributed randomly at the interval 0,2 , M
is the harmonics number (if M , a mathematical
fractal is obtained).
2. SYSTEM SPECTRAL ANALYSIS BASES
One of the most effective modern signal analysis
methods, called as the system spectral analysis, has been
proposed in 2007 by the authors of the paper [4].
The system spectral analysis is based on the simul-
taneous application of set of linear and non-linear inte-
gral transforms [1, 4, 5]. In first group there are the con-
tinuous wavelet transform (CWT), the analytical wave-
let transform (AWT), the Gabor transform (GT), the
adaptive Fourier transform (AFT) and the short-time
Fourier transform (STFT). Second group includes some
members of the Cohen’s class of square non-linear inte-
gral transforms, namely the Fourier spectrogram (FS),
the Wigner transform (WiT), the Choi-Williams trans-
form (ChWT) and the Born-Jordan transform (BJT). In
addition to the module of spectral density function
(SDF), for every transform also the skeletons, ener-
gograms, dispersions of the SDF module for linear
transforms and standard deviations of the SDF module
for non-linear transforms are used.
The basic idea of the system spectral analysis is the
compensation of disadvantages of the some transforms
due to advantages of other ones.
A quantity and set of integral transforms, used in the
systems spectral analysis, can change in the future.
For the system spectral analysis performing the sys-
tem of computer mathematics MATLAB including
packages Wavelet Toolbox, Time-Frequency Toolbox,
Wave Laboratory and some original software for
MATLAB created by authors were used.
3. ANALYSIS RESULTS
Considering the results of the system spectral analy-
sis of model FUWB signal with the fractal dimension
1.5D (Fig. 1,a), lets demonstrate the validating of
our transform choice.
The linear transform selection was based on the such
reasons. The CWT SDF (Fig. 1,b) has a good time-
frequency resolution, its basis is self-similar, there are
many different wavelets allowing choosing the optimal
one for each signal analyzed. The argument of the com-
plex AWT SDF (Fig. 1,d) has more abilities for the ana-
lyzing of the signals with peculiarities than the CWT
has. Therefore, AWT is appears to be very useful addi-
tion to the CWT. The GT SDF (Fig. 1,e) has the best
time-frequency localization in the middle of all time-
frequency transforms.
mailto:1gisone@gmail.com
ISSN 1562-6016. ВАНТ. 2015. №4(98) 245
Fig. 1. The analysis results of model FUWB signal: a, j – signal in time domain; b – CWT SDF with Morlet
wavelet; c – CWT SDF skeleton; d – phase of complex coefficients of AWT with cgau1 wavelet;
e – GT SDF module; f – CWT SDF energogram; g – dispersion of CWT SDF coefficients; h – GT SDF ener-
gogram; i – dispersion of GT SDF module; k – AFT SDF module; l – AFT SDF skeleton; m – STFT SDF mod-
ule;
n – STFT SDF skeleton; o – AFT SDF energogram; p – dispersion of AFT SDF module;
r – STFT SDF energogram; s – dispersion of AFT SDF module
ISSN 1562-6016. ВАНТ. 2015. №4(98) 246
Fig. 2. The analysis results of model FUWB signal: a, j – signal in time domain; b – WiT SDF; c – WiT SDF
skeleton; d – FS SDF; e – FS SDF skeleton; f – WiT SDF energogram; g – dispersion of WiT SDF coefficients;
h – FS SDF energogram; i – dispersion of FS SDF module; k – ChWT SDF module; l – ChWT SDF skeleton;
m – BJT SDF module; n – BJT SDF skeleton; o – ChWT SDF energogram;
p – dispersion of ChWT SDF module; r – BJT SDF energogram; s – dispersion of BJT SDF module
ISSN 1562-6016. ВАНТ. 2015. №4(98) 247
The AFT SDF (Fig. 1,k) is appeared to be another
useful look at the signal time-frequency structure.
Sometimes, the AFT comes to the AWT, but in a num-
ber of cases it has an independent sense, in particular,
when the non-symmetrical window functions have been
used. The STFT SDF (Fig. 1,m) is appeared to be a
good addition to the other ones. It is useful especially
for the narrow-band signal analysis.
The non-linear transform selection was based on such
reasons. The WiT SDF (Fig. 2,b) has good time-
frequency resolution which is better than one for linear
transforms. The ChWT SDF (Fig. 2,k) has the parame-
ter allowing to control by level of the cross-terms ap-
pearing in the WiT SDF in case of the multi-component
signal analysis. Another way of the cross-term influence
reduction is given by the BJT SDF (Fig. 2,m) applica-
tion. The FS SDF (Fig. 2,d) has the worst time-
frequency resolution, but it has no interference struc-
tures for multi-component signals. Being the limit result
of the WiT averaging in time- and frequency domains,
the FS allows effectively selecting the really existent
signals and the cross-terms during the WiT interpreta-
tion process. Moreover, all non-linear transforms are
appeared to be useful for the analysis of the signals in
case of the non-Gaussian noise presence.
Some words about other numerical characteristics.
The skeleton is defined as the set of the local maxima
lines of the SDF module. Some experts believe that in
skeleton there is all possible information about signal
investigated.
The distribution of the energy of the analyzed signal
along the period or frequency variable is given exactly
by the energogram. Some another view is given by the
dispersion of module of the SDF coefficients for linear
transforms and the mean-square deviation of module of
the SDF coefficients for non-linear ones.
The time-frequency structure of the model FUWB sig-
nal was found to be fractal. This is demonstrated partic-
ularly bright by the SDFs and skeletons of the linear
integral transforms, namely the CWT and the AWT.
The non-linear transforms results are appeared to be
slightly worse.
CONCLUSIONS
• The system spectral analysis as a new integrated
signal analysis method based on the simultaneous
application of linear and non-linear integral trans-
forms got further development.
• The system spectral analysis was shown to be able to
perform a complex research of a signal, compensat-
ing the disadvantages of some used integral trans-
forms by advantages other ones.
• On the example of study of the model FUWB signal
the efficiency of the system spectral analysis as a
new signal analysis method was shown.
REFERENCES
1. O.V. Lazorenko, L.F. Chernogor. Ultrawideband
Signals and Processes: Monograph. Kharkov:
V.N. Karazin Kharkiv National University, 2009.
2. L.F. Chernogor. About Nonlinearity in Nature and
Science: Monograph. Kharkov: V.N. Karazin
Kharkiv National University, 2008.
3. O.V. Lazorenko, A.A Potapov, L.F. Chernogor.
Fractal Ultrawideband Signals // Informational secu-
rity: the encryption methods / Ed.-in-ch.
E.M. Suharev. Moscow: “Radiotechnika”, 2011.
4. O.V. Lazorenko, L.F. Chernogor. System Spectral
Analysis of Signals: Theoretical Bases and Practical
Applications // Radio Physics and Radio Astronomy
(12). 2007, № 2, p. 162-181.
5. L.F. Chernogor, O.V. Lazorenko. System Spectral
Analysis of Model Ultra-Wideband Signals // Proc.
Ultrawideband and Ultrashort Impulse Signals. Se-
vastopol, Ukraine, 2012, p. 243-245.
Article received 01.06.2015
СИСТЕМНЫЙ СПЕКТРАЛЬНЫЙ АНАЛИЗ ФРАКТАЛЬНЫХ СВЕРХШИРОКОПОЛОСНЫХ
СИГНАЛОВ
Л.Ф. Черногор, С.Г. Кравченко, О.В. Лазоренко
Кратко рассмотрены теоретические основы и практические особенности системного спектрального ана-
лиза. Разъяснена необходимость и целесообразность одновременного применения различных линейных и
нелинейных интегральных преобразований для проведения системного спектрального анализа. Показано,
что использование системного спектрального анализа для исследования время-частотной структуры фрак-
тальных сверхширокополосных сигналов является полезным и эффективным.
СИСТЕМНИЙ СПЕКТРАЛЬНИЙ АНАЛІЗ ФРАКТАЛЬНИХ НАДШИРОКОСМУГОВИХ
СИГНАЛІВ
Л.Ф. Чорногор, С.Г. Кравенко, О.В. Лазоренко
Стисло розглянуто теоретичні засади та практичні особливості системного спектрального аналізу.
Роз’яснено необхідність і доцільність одночасного використання різних лінійних і нелінійних інтегральних
перетворень для проведення системного спектрального аналізу. Продемонстровано, що застосування систе-
много спектрального аналізу для дослідження часо-частотної структури фрактальних надширокосмугових
сигналів є корисним та ефективним.
introduction
1. fractal ultra-wideband signal models
2. system spectral analysis bases
3. analysis results
Conclusions
references
Системный спектральный анализ фрактальных сверхширокополосных сигналов
Системний спектральний аналіз фрактальних надширокосмугових сигналів
|