Relevant bibliographies by topics / Cyclostationary process

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Cyclostationary process'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 May 2022

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Journal articles on the topic "Cyclostationary process"

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Konstant, D. G., and V. I. Piterbarg. "Extreme values of the cyclostationary Gaussian random process." Journal of Applied Probability 30, no. 1 (1993): 82–97. http://dx.doi.org/10.2307/3214623.

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In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.
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Konstant, D. G., and V. I. Piterbarg. "Extreme values of the cyclostationary Gaussian random process." Journal of Applied Probability 30, no. 01 (1993): 82–97. http://dx.doi.org/10.1017/s0021900200044016.

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In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula is established for and all x > 0.
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Lyridis, Dimitrios V., Anastassios N. Perakis, and Michael G. Parsons. "Structural Reliability Analysis of Marine Diesel Engine Shafting Systems: An Equivalent Stationary Process Approach to the Level Crossing Problem." Journal of Ship Research 38, no. 03 (1994): 253–58. http://dx.doi.org/10.5957/jsr.1994.38.3.253.

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This paper is concerned with the level crossing problem of a stress above some limit. The problem arises when the structural reliability of a diesel engine shafting system is examined. The first excursion failure probability is derived for the case that the stress on the shaft is a one-frequency cyclostationary random process. A new method is introduced where the cyclostationary random process is replaced with an equivalent stationary one, defined to have an envelope process with the same upcrossing rate as the envelope of the original cyclostationary process. Both processes are assumed to have the same probability of upcrossing a specific threshold. The agreement between this approach, which results in an analytical expression, and the "exact," computationally time-consuming "Markov approach" presented in earlier work is excellent.
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Kuznetsov, Yury V., Andrey B. Baev, Maxim A. Konovalyuk, and Anastasia A. Gorbunova. "Cyclostationary Crosstalk Cancelation in High-Speed Transmission Lines." Applied Sciences 11, no. 17 (2021): 7988. http://dx.doi.org/10.3390/app11177988.

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The theoretical and experimental evaluation of the cyclostationary random data transferring process corrupted by the individually and jointly cyclostationary crosstalk interference is presented. The interference and the message signals were measured by the real time digital oscilloscope. Autocorrelation functions were evaluated by synchronous cyclic averaging procedure. The analyzed periodic two-dimensional impulse response of the time-varying filter allows to obtain the output random process with the same cyclic frequency at the output of the filter by separation of orthogonal stationary waveforms constituting the input cyclostationary random process (CSRP). The filtering of the measured random process was implemented by the cyclic Wiener filter. The evaluation of the two-dimensional autocorrelation function and eye diagrams at the output of the cyclic Wiener filter showed significant reduction of the independent interference components in the estimated message signal.
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Napolitano, Antonio. "Modeling the Electrocardiogram as Oscillatory Almost-Cyclostationary Process." IEEE Access 10 (2022): 13193–209. http://dx.doi.org/10.1109/access.2022.3147500.

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Antoni, J., and R. B. Randall. "Differential Diagnosis of Gear and Bearing Faults." Journal of Vibration and Acoustics 124, no. 2 (2002): 165–71. http://dx.doi.org/10.1115/1.1456906.

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This paper deals with the vibration-based diagnosis of rolling element bearings in the presence of strong interfering gear signals, such as is typical of helicopter gearboxes. The key idea consists in recognizing gear signals as purely periodic, whereas bearing signals experience some randomness and are close to cyclostationary, i.e. with a periodic bivariate autocorrelation function. This assertion is demonstrated by introducing a comprehensive model for the vibration generating process of bearing faults: distinctions are made between localized and distributed faults, between cyclostationary and pseudo-cyclostationary processes, and between additive and multiplicative interactions with gear signals. Finally, an original diagnostic procedure is proposed and its performance illustrated using simulated, experimental and actual cases.
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CAHYO, HENDRY, DWI ARYANTA, and NASRULLAH ARMI. "Kinerja Spectrum Sensing Dengan Metode Cyclostationary Feature Detector Pada Radio Kognitif." ELKOMIKA: Jurnal Teknik Energi Elektrik, Teknik Telekomunikasi, & Teknik Elektronika 1, no. 1 (2013): 26. http://dx.doi.org/10.26760/elkomika.v1i1.26.

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ABSTRAKPerkembangan dalam dunia telekomunikasi nirkabel terutama spektrum frekuensi adalah hal yang perlu mendapatkan perhatian penting. Spektrum frekuensi merupakan sumber daya yang terbatas, penggunaannya harus dilakukan secara efisien dan se-maksimal mungkin. Penelitian ini membahas teknik spectrum sensing pada radio kognitif untuk menghadapi masalah keterbatasan penggunaan spektrum frekuensi. Radio kognitif merupakan sistem radio cerdas yang bisa mengatur parameternya seperti frekuensi kerja, daya pancar, dan skema modulasi secara optimal dalam melakukan proses komunikasi. Spectrum sensing merupakan teknik untuk memaksimalkan penggunaan spektrum frekuensi. Penelitian ini membandingkan kinerja metode cyclostationary feature detection dan metode energy detection pada teknik spectrum sensing menggunakan software matlab sehingga dapat diketahui bahwa kinerja cyclostationary feature detection untuk nilai Pd = 0,85 lebih handal sebesar 0,2 untuk fungsi probability of false dan lebih handal sebesar 2 dB untuk fungsi signal to noise ratio daripada energy detection.Kata kunci: radio kognitif, spectrum sensing, cyclostationary feature detection, energy detection, probability of false alarm. ABSTRACTDevelopments in the world of wireless telecommunications specially frequency spectrum is an important thing to get attention. Frequency spectrum is afinite resource, its use must be efficiently and as maximum as possible. This study discuss the technique of spectrum sensing in cognitive radio to faces the problem using restrictiveness of frequency spectrum. Cognitive radio is a smart radio system that can adjust its parameters like work frequency, emission power, and modulation scheme are optimal in the communication process. Spectrum sensing is a technique to maximize the use of the frequency spectrum. This study compared performance of cyclostationary feature detection methodh with energy detection methodh in spectrum sensing technique using matlab software so ascertainable that cyclostationary feature detection performance for Pd value 0,85 better about 0,2 for probability of false alarm function and better about 2 dB for signal to noise ratio function than energy detection.Keywords: cognitif radio, spectrum sensing, cyclostationary feature detection, energy detection, probability of false alarm.
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Shevgunov, Timofey Ya. "SHAPING OPERATOR TECHNIQUE FOR MODELLING CYCLOSTATIONARY RANDOM PROCESSES." T-Comm 15, no. 8 (2021): 4–12. http://dx.doi.org/10.36724/2072-8735-2021-15-8-4-12.

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The paper proposes the shaping operator technique for modelling cyclostationary random process (CSRP) which belong to the class of second-order processes being described by the parametric pulse train model. Generating CSRP is expressed as the propagation result of the specially chosen elementary CSRP through the linear time-invariant system with a known impulse response. The paper describes the approach to forming the elementary CSRP based on the train made of Dirac delta-function uniformly following in time domain with constant step and defining the desired structural periodicity of the process being modelled. The analytical expressions for the main characteristics used for describing cyclostationary properties of the elementary process, including two-dimensional, cyclic and spectral correlation functions, were obtained. In addition to the case of the elementary CSRP with correlated weighting coefficients of delta-functions, the case of statistically independent coefficients was considered. It was shown that utilization of the spectral correlation function (SCF) for describing the cyclic property reveals the explicit analytical relation between characteristics of the elementary and modelled CSRPs provided the filter frequency response is known. The paper presents the comparative example which describes the modelling of two CSRPs: one of them was chosen as the train of rectangle pulses which is pulse amplitude modulated by stationary random time series, while the other is considered as a signal formed by the method of direct sequence spread spectrum. The chosen short-length Barker sequence as the code allowed performing visual comparison between absolute value of SCF components taken at the cyclic frequencies multiple of the chip frequency and cyclic frequencies multiple of the symbol frequency. The future development of the methods proposed in the paper opens the road to improving the performance of modern radar and telecommunication systems by means of utilizing cyclic frequencies which are non-random parameters describing the structural properties of signals under processing.
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Lisboa de Souza, Antonio Augusto, Emmanuel Dupouy, Jean-Christophe Nallatamby, Michel Prigent, and Juan Obregon. "Experimental characterization of the cyclostationary low-frequency noise of microwave semiconductor devices under large signal operation." International Journal of Microwave and Wireless Technologies 2, no. 2 (2010): 225–33. http://dx.doi.org/10.1017/s1759078710000140.

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This paper presents a detailed experimental analysis of the cyclostationary properties of low-frequency (LF) noise sources of microwave bipolar devices, in order to improve the LF noise description in compact models. Such models are used to help designers on predicting circuit performances such as phase and amplitude noise in oscillators. We start by reviewing the most relevant experimental and simulation results on the subject, and then investigate the model of conductance fluctuations proposed to explain the 1/f noise of carbon resistors. This simple linear case serves as a basis for understanding the complex case of a non-linear device under large-signal periodic operation. We then present the large-signal small-signal analysis of a pumped junction, focusing on the process of converting the fundamental LF noise process, a current fluctuation, into voltage fluctuations. We show why a stationary noise model would lead to an increase of the voltage noise observed around DC when the device is pumped, while the voltage noise would decrease if a cyclostationary model was used. A great amount of experimental data is presented not only to support our analysis, but also as a mean to distinguish between the two noise processes under consideration: stationary or cyclostationary. The goal of our noise measurement technique was to maximize the difference between those two concepts. Throughout the paper, we revisit some known concepts and show how some experimental results may lead to misinterpretations.
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Abakasanga, Emeka, Nir Shlezinger, and Ron Dabora. "On the Rate-Distortion Function of Sampled Cyclostationary Gaussian Processes." Entropy 22, no. 3 (2020): 345. http://dx.doi.org/10.3390/e22030345.

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Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it is applied to discrete-time (DT) processes obtained by sampling the CT processes. When sampling is applied to a CT WSCS process, the statistics of the resulting DT process depends on the relationship between the sampling interval and the period of the statistics of the CT process: When these two parameters have a common integer factor, then the DT process is WSCS. This situation is referred to as synchronous sampling. When this is not the case, which is referred to as asynchronous sampling, the resulting DT process is wide-sense almost cyclostationary (WSACS). The sampled CT processes are commonly encoded using a source code to facilitate storage or transmission over wireless networks, e.g., using compress-and-forward relaying. In this work, we study the fundamental tradeoff between rate and distortion for source codes applied to sampled CT WSCS processes, characterized via the rate-distortion function (RDF). We note that while RDF characterization for the case of synchronous sampling directly follows from classic information-theoretic tools utilizing ergodicity and the law of large numbers, when sampling is asynchronous, the resulting process is not information stable. In such cases, the commonly used information-theoretic tools are inapplicable to RDF analysis, which poses a major challenge. Using the information-spectrum framework, we show that the RDF for asynchronous sampling in the low distortion regime can be expressed as the limit superior of a sequence of RDFs in which each element corresponds to the RDF of a synchronously sampled WSCS process (yet their limit is not guaranteed to exist). The resulting characterization allows us to introduce novel insights on the relationship between sampling synchronization and the RDF. For example, we demonstrate that, differently from stationary processes, small differences in the sampling rate and the sampling time offset can notably affect the RDF of sampled CT WSCS processes.
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Dissertations / Theses on the topic "Cyclostationary process"

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Jha, Akhilesh K. "Cyclostationary Random Vibration of a Ship Propeller and a Road Vehicle." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/34486.

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A special class of nonstationary processes with periodically varying statistics, called cyclostationary (CS), is investigated. These processes are encountered in many engineering problems involving rotating machinery such as turbines, propellers, helicopter rotors, and diesel engines. We analyze a cyclostationary process model in order to show its advantages compared to a traditional stationary process model and present a methodology for calculating the statistics of the response of a linear system subjected to CS excitations. We demonstrate that a CS model estimates the statistics of the response of a linear dynamic system subjected to CS excitations more accurately by considering (1) a vehicle traveling on a rough road and (2) a propeller rotating in the wake of a ship in the presence of turbulence. In the case of the vehicle, the road consists of concrete plates of fixed length. We model the road excitation using a CS process and calculate the standard deviation (root mean square) of the vehicle response. In the case of the ship propeller, we calculate the hydrodynamic forces acting on the propeller using the vortex panel method and the vortex theory of propeller. Considering the randomness in the axial and the tangential components of velocity, we calculate the mean and the covariance of the forces. This analysis shows that the hydrodynamic forces acting on the propeller are CS processes. Then we perform finite element analysis of the propeller and calculate the mean and the standard deviation of the blade response. We do the parametric analysis to demonstrate the effects of some physical quantities such as the standard deviation, the correlation coefficient, the decorrelation time, and the scale of turbulence of the axial and the tangential components of the wake velocity on the standard deviation of the blade deflection. We found that the CS model yields the time-wise variation of the statistics of the excitation and the response (e.g., the root mean square) and their peaks correctly. This is important information for the calculation of probability of failure of the propeller. A traditional stationary model cannot provide this information.<br>Master of Science
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Франчевська, Галина Іванівна, та Halyna Franchevska. "Комп’ютерна система розпізнавання електрокардіосигналу плоду". Master's thesis, Тернопільський національний технічний університет імені Івана Пулюя, 2020. http://elartu.tntu.edu.ua/handle/lib/33262.

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Кваліфікаційну роботу виконано на кафедрі біотехнічних систем Тернопільського національного технічного університету імені Івана Пулюя<br>Дипломну роботу присвячено розробці алгоритму та системи розпізнавання електрокардіосигналів плоду у комп’ютерних електрокардіографах. На базі фільтрового методу обробки електрокардіосигналу плоду з врахуванням взаємокореляції розроблено комп’ютерну систему розпізнавання електрокардіосигналів плоду на фоні різноманітних артефактів. Комп’ютерну систему виявлення електрокардіосигналу плоду розроблено із використанням програмного забезпечення MATLAB і SIMULINK.<br>The master’s thesis is devoted to an algorithm and system for detecting fetal electrocardiographic signals in computer electrocardiographs. Based on the filter method of fetal electrocardiographic processing, taking into the correlation, a computer system for detecting fetal electrocardiographic signals against the background of various artifacts has been developed. The computer system for detecting fetal electrocardiographic signals was developed using MATLAB and SIMULINK software.<br>ЗМІСТ СПИСОК СКОРОЧЕНЬ 8 ВСТУП 9 РОЗДІЛ 1 АНАЛІТИЧНА ЧАСТИНА 11 1.1 Особливості анатомії та електрофізіології серця плоду 11 1.2 Медико–біологічні методи дослідження ССС плоду 16 1.2.1 Ультразвукова доплерографія 15 1.2.2 Аускультація 16 1.2.3 Кардіотокографія 18 1.2.4 Електрокардіографія 18 1.3 Методи виділення ЕКС плоду 18 1.4 Комп’ютерні електрокардіографи для виявлення електрокардіосигналу плоду 20 1.4.1 KAGUWI KGW–6000 20 1.4.2 КАРДИОЛАБ БЭБИ–Кард 22 1.5 Висновки до розділу 1 23 РОЗДІЛ 2 ОСНОВНА ЧАСТИНА 24 2.1 CP –періодично корельований випадковий процес 24 2.2 Обґрунтування вибору CP як математичної моделі ЕКС плоду 26 2.3 Математична модель ЕКС плоду 27 2.4 Висновки до розділу 2 34 РОЗДІЛ 3 НАУКОВО–ДОСЛІДНА ЧАСТИНА 35 3.1 Алгоритм розпізнавання ЕКС плоду 35 3.2 Модель SIMULINK 36 3.3 Метод найменших квадратів 37 3.4 Програмна реалізація 37 3.5 Використані методи для виокремлення ЕКС плоду 41 3.6 Результати 42 3.7 Техніка диференціації для виявлення QRS 46 3.8 Розрахунок витрат на проведення НДР 50 3.8.1 Затрати на оплату праці 50 3.8.2 Затрати на соціальні заходи 52 3.8.3 Обладнання, що необхідне для виконання досліджень 52 3.8.4 Енергоносії, котрі потрібні для проведення досліджень 53 3.8.5 Затрати на службові відрядження 54 3.8.6 Планова калькуляція. Кошторисна вартість теми 55 3.8.7 НДР та її науково–технічна ефективність 56 3.9 Висновки до розділу 3 57 РОЗДІЛ 4 СПЕЦІАЛЬНА ЧАСТИНА 60 4.1 Методика проведення досліджень 60 4.2 Обґрунтування теми вибору УДК дослідження 62 4.3 Висновки до розділу 4 63 РОЗДІЛ 5 ОХОРОНА ПРАЦІ ТА БЕЗПЕКА В НАДЗВИЧАЙНИХ СИТУАЦІЯХ 64 5.1 Охорона праці 64 5.2 Безпека в надзвичайних ситуаціях 66 5.3 Висновки до розділу 5 69 ЗАГАЛЬНІ ВИСНОВКИ 70 ПЕРЕЛІК ПОСИЛАНЬ 71 ДОДАТКИ 76 Додаток А 77 Додаток В 79
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Datta, Gupta Syamantak. "On MMSE Approximations of Stationary Time Series." Thesis, 2013. http://hdl.handle.net/10012/8143.

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In a large number of applications arising in various fields of study, time series are approximated using linear MMSE estimates. Such approximations include finite order moving average and autoregressive approximations as well as the causal Wiener filter. In this dissertation, we study two topics related to the estimation of wide sense stationary (WSS) time series using linear MMSE estimates. In the first part of this dissertation, we study the asymptotic behaviour of autoregressive (AR) and moving average (MA) approximations. Our objective is to investigate how faithfully such approximations replicate the original sequence, as the model order as well as the number of samples approach infinity. We consider two aspects: convergence of spectral density of MA and AR approximations when the covariances are known and when they are estimated. Under certain mild conditions on the spectral density and the covariance sequence, it is shown that the spectral densities of both approximations converge in L2 as the order of approximation increases. It is also shown that the spectral density of AR approximations converges at the origin under the same conditions. Under additional regularity assumptions, we show that similar results hold for approximations from empirical covariance estimates. In the second part of this dissertation, we address the problem of detecting interdependence relations within a group of time series. Ideally, in order to infer the complete interdependence structure of a complex system, dynamic behaviour of all the processes involved should be considered simultaneously. However, for large systems, use of such a method may be infeasible and computationally intensive, and pairwise estimation techniques may be used to obtain sub-optimal results. Here, we investigate the problem of determining Granger-causality in an interdependent group of jointly WSS time series by using pairwise causal Wiener filters. Analytical results are presented, along with simulations that compare the performance of a method based on finite impulse response Wiener filters to another using directed information, a tool widely used in literature. The problem is studied in the context of cyclostationary processes as well. Finally, a new technique is proposed that allows the determination of causal connections under certain sparsity conditions.
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Book chapters on the topic "Cyclostationary process"

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Hurd, Harry, and Timo Koski. "Cyclostationary Arrays." In Stochastic Processes and Functional Analysis. CRC Press, 2004. http://dx.doi.org/10.1201/9780203913574.ch9.

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Napolitano, Antonio. "Almost-cyclostationary signal processing." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00014-5.

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Napolitano, Antonio. "Generalized almost-cyclostationary signals." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00024-8.

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Napolitano, Antonio. "Oscillatory almost-cyclostationary signals." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00026-1.

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Napolitano, Antonio. "Higher-order cyclostationarity." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00015-7.

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"Front Matter." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00002-9.

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"Copyright." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00003-0.

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"Contents." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00005-4.

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"About the Author." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00006-6.

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Napolitano, Antonio. "Preface." In Cyclostationary Processes and Time Series. Elsevier, 2020. http://dx.doi.org/10.1016/b978-0-08-102708-0.00007-8.

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Conference papers on the topic "Cyclostationary process"

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D’Elia, Gianluca, Simone Delvecchio, Marco Cocconcelli, and Giorgio Dalpiaz. "Application of Cyclostationary Indicators for the Diagnostics of Distributed Faults in Ball Bearings." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12804.

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This paper deals with the detection of distributed faults in ball bearings. In literature most of the authors focus their attention on the detection of incipient localized defects. In that case classical techniques (i.e. statistical parameters, envelope analysis) are robust in recognizing the presence of the fault and its characteristic frequency. In this paper the authors focalize their attention on bearings affected by distributed faults, due to the progressive growing of surface wear or to low-quality manufacturing process. These faults can not be detected by classical techniques; in fact, in this case the signal does not contain impulses at the fault characteristic frequency, but more complex components with strong non-stationary contents. Distributed faults are here detected by means of advanced tools directly derived from the theory of cyclostationarity. In particular three metrics — namely Integrated Cyclic Coherence (ICC), Integrated Cyclic Modulation Coherence (ICMC) and Indicator of Second-Order Cyclostationarity (ICS2x) — have been calculated in order to condense the information given by the cyclostationary analysis and to help the analyst in detecting the fault in a fast fault diagnosis procedure. These indicators are applied on actual signals captured on a test rig where a degreased bearing running under radial load developed accelerated wear. The results indicated that all the three cyclostationary indicators are able to detect both the appearance of a localized fault and its development in a distributed fault, whilst the usual approach fails as the fault grows.
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Napolitano, Antonio. "Aircraft Acoustic Signal Modeled as Oscillatory Almost-Cyclostationary Process." In 2020 28th European Signal Processing Conference (EUSIPCO). IEEE, 2021. http://dx.doi.org/10.23919/eusipco47968.2020.9287381.

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Gryllias, Konstantinos, Simona Moschini, and Jerome Antoni. "Application of Cyclo-Non-Stationary Indicators for Bearing Monitoring Under Varying Operating Conditions." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64443.

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Condition monitoring assesses the operational health of rotating machinery, in order to provide early and accurate warning of potential failures such that preventative maintenance actions may be taken. To achieve this target, manufacturers start taking on the responsibilities of engine condition monitoring, by embedding health monitoring systems within each engine unit and prompting maintenance actions when necessary. Several types of condition monitoring are used including oil debris monitoring, temperature monitoring and vibration monitoring. Among them, vibration monitoring is the most widely used technique. Machine vibro-acoustic signatures contain pivotal information about its state of health. The current work focuses on one part of the diagnosis stage of condition monitoring for engine bearing health monitoring as bearings are critical components in rotating machinery. A plethora of signal processing tools and methods applied at the time domain, the frequency domain, the time-frequency domain and the time-scale domain have been presented in order to extract valuable information by proposing different diagnostic features. Among others, an emerging interest has been reported on modeling rotating machinery signals as cyclostationary, which is a particular class of non-stationary stochastic processes. A process x(t) is said to be nth-order cyclostationary with period T if its nth-order moments exist and are periodic with period T. Several tools, such as the Spectral Correlation Density (SCD) and the Cyclic Modulation Spectrum (CMS) can be used in order to extract interesting information concerning the cyclic behavior of cyclostationary signals. In order to measure the cyclostationarity from order 1 to 4, concise and global indicators have been proposed. However, in a number of applications such as aircraft engines and wind turbines the characteristic vibroacoustic signatures of rotating machinery depend on the operating conditions of the rotational speed and/or the load. During the last decades fault diagnostics of rotating machinery under variable speed/load has attracted a lot of interest. The classical cyclostationary tools can be used under the assumption that the speed of machinery is constant or nearly constant, otherwise the vibroacoustic signal becomes cyclo-non-stationary. In order to overcome this limitation a generalization of both SCD and CMS functions have been proposed displaying cyclic Order versus Frequency. The goal of this paper is to propose a novel approach for the analysis of cyclo-nonstationary signals based on the generalization of indicators of cyclostationarity in order to cover the speed varying conditions. The proposed indicators of cyclo-non-stationarity (ICNS) are expected to summarize the information at various statistical orders and at lower computational cost compared to the Order-Frequency SCD or CMS. This generalization is realized by introducing a new speed-dependent angle averaging operator. The effectiveness of the approach is evaluated on an acceleration signal captured on the casing of an aircraft engine gearbox, provided by SAFRAN, in the frames of SAFRAN contest which took place at the Surveillance 8 International Conference.
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Ramirez, David, Peter J. Schreier, Javier Via, Ignacio Santamaria, and Louis L. Scharf. "A regularized maximum likelihood estimator for the period of a cyclostationary process." In 2014 48th Asilomar Conference on Signals, Systems and Computers. IEEE, 2014. http://dx.doi.org/10.1109/acssc.2014.7094815.

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5

Mauricio, Alexandre, Dustin Helm, Markus Timusk, Jerome Antoni, and Konstantinos Gryllias. "Novel Cyclo-Non-Stationary Indicators for Monitoring of Rotating Machinery Operating Under Speed and Load Varying Conditions." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15245.

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Abstract Condition monitoring arises as a valuable industrial process in order to assess the health of rotating machinery, providing early and accurate warning of potential failures and allowing for the planning and effective realization of preventative maintenance actions. Nowadays machinery (gas turbines, wind turbines etc.) manufacturers adopt new business models, providing not only the equipment itself but additionally taking on responsibilities of condition monitoring, by embedding sensors and health monitoring systems within each unit and prompting maintenance actions when necessary. Among others, rolling element bearings are one of the most critical components in rotating machinery. In complex machines the failure indications of an early bearing damage are weak compared to other sources of excitations (e.g. gears, shafts, rotors etc.). Vibration analysis is most widely used and various methods have been proposed, including analysis in the time and frequency domain. In a number of applications, changes in the operating conditions (speed/load) influence the vibration sources and change the frequency and amplitude characteristics of the vibroacoustic signature, making them nonstationary. Under changing environments, where speed and load vary, the assumption of quasi-stationary is not appropriate and as a result a number of time-frequency and time-order representations have been introduced, such as the Short Time Fourier Transform and the Wavelets. Recently an emerging interest has been focused on modelling rotating machinery signals as cyclostationary, which is a particular class of non-stationary stochastic processes. The classical cyclostationary tools, such as the Cyclic Spectral Correlation Density (CSCD) and the Cyclic Modulation Spectrum (CMS), can be used in order to extract interesting information about the cyclic behavior of cyclostationary signals, only under the assumption that the speed of machinery is constant or nearly constant. Global diagnostic indicators have been proposed as a measure of cyclostationarity under steady operating conditions. In order to overcome this limitation a generalization of both SCD and CMS functions have been proposed displaying cyclic Order versus Frequency as well as diagnostic indicators of cyclo-non-stationarity in order to cover the speed varying operating conditions. The scope of this paper is to propose a novel approach for the analysis of cyclo-non-stationary signals based on the generalization of indicators of cyclo-non-stationarity in order to cover the simultaneous and independently varying speed and load operating conditions. The effectiveness of the approach is evaluated on simulated and real signals captured on a dedicated test rig.
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Yeo, Jeongho, and Joon Ho Cho. "Asymptotically optimal low-complexity estimation of sampled improper-complex second-order cyclostationary random process." In 2013 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2013. http://dx.doi.org/10.1109/wcnc.2013.6555012.

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Stefanakos, Christos N., and Konstandinos A. Belibassakis. "Nonstationary Stochastic Modelling of Multivariate Long-Term Wind and Wave Data." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67461.

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In the present work, a nonstationary stochastic model, which is suitable for the analysis and simulation of multivariate time series of wind and wave data, is being presented and validated. This model belongs to the class of periodically correlated stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First, the time series is appropriately transformed to become Gaussian using the Box-Cox transformation. Then, the series is decomposed, using an appropriate seasonal standardization procedure, to a periodic (deterministic) mean value and a (stochastic) residual time series multiplied by a periodic (deterministic) standard deviation. The periodic components are estimated using appropriate time series of monthly data. The residual stochastic part, which is proved to be stationary, is modelled as a VARMA process. This way the initial process can be given the structure of a multivariate periodically correlated process. The present methodology permits a reliable reproduction of available information about wind and wave conditions, which is required for a number of applications.
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Bin Wu, Minjie Wang, and Yuegang Luo. "Notice of Retraction: Cyclostationarity and CHMM based bearing fault diagnosis approach in start-up process." In 2010 2nd International Conference on Computer Engineering and Technology (ICCET). IEEE, 2010. http://dx.doi.org/10.1109/iccet.2010.5486117.

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