Search results for: periodogram

Authors: Yaeji Lim, Hee-Seok Oh

Abstract:

The coherence analysis measures the linear time-invariant relationship between two data sets and has been studied various fields such as signal processing, engineering, and medical science. However classical coherence analysis tends to be sensitive to outliers and focuses only on mean relationship. In this paper, we generalized cross periodogram to quantile cross periodogram and provide richer inter-relationship between two data sets. This is a general version of Laplace cross periodogram. We prove its asymptotic distribution under the long range process and compare them with ordinary coherence through numerical examples. We also present real data example to confirm the usefulness of quantile coherence analysis.

Keywords: coherence, cross periodogram, spectrum, quantile

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Authors: Mesut BALIBEY, Serpil TÜRKYILMAZ

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A popular topic in the econometrics and time series area is the cointegrating relationships among the components of a nonstationary time series. Engle and Granger’s least squares method and Johansen’s conditional maximum likelihood method are the most widely-used methods to determine the relationships among variables. Furthermore, a method proposed to test a unit root based on the periodogram ordinates has certain advantages over conventional tests. Periodograms can be calculated without any model specification and the exact distribution under the assumption of a unit root is obtained. For higher order processes the distribution remains the same asymptotically. In this study, in order to indicate advantages over conventional test of periodograms, we are going to examine a possible relationship between tourism and economic growth during the period 1999:01-2010:12 for Turkey by using periodogram method, Johansen’s conditional maximum likelihood method, Engle and Granger’s ordinary least square method.

Keywords: cointegration, economic growth, periodogram ordinate, tourism

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Authors: Sadaf Nawaz, Adnan Ahmed Khan, Asad Mahmood, Chaudhary Farrukh Javed

Abstract:

Classically, an energy detector is implemented in time domain (TD). However, frequency domain (FD) based energy detector has demonstrated an improved performance. This paper presents a comparison between the two approaches as to analyze their pros and cons. A detailed performance analysis of the classical TD energy-detector and the periodogram based detector is performed. Exact and approximate mathematical expressions for probability of false alarm (Pf) and probability of detection (Pd) are derived for both approaches. The derived expressions naturally lead to an analytical as well as intuitive reasoning for the improved performance of (Pf) and (Pd) in different scenarios. Our analysis suggests the dependence improvement on buffer sizes. Pf is improved in FD, whereas Pd is enhanced in TD based energy detectors. Finally, Monte Carlo simulations results demonstrate the analysis reached by the derived expressions.

Keywords: cognitive radio, energy detector, periodogram, spectrum sensing

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Authors: Rafik Djemili, Hocine Bourouba, M. C. Amara Korba

Abstract:

In this paper, we present a method in order to classify EEG signals for Brain-Computer Interfaces (BCI). EEG signals are first processed by means of spectral estimation methods to derive reliable features before classification step. Spectral estimation methods used are standard periodogram and the periodogram calculated by the Welch method; both methods are compared with Logarithm of Band Power (logBP) features. In the method proposed, we apply Linear Discriminant Analysis (LDA) followed by Support Vector Machine (SVM). Classification accuracy reached could be as high as 85%, which proves the effectiveness of classification of EEG signals based BCI using spectral methods.

Keywords: brain-computer interface, motor imagery, electroencephalogram, linear discriminant analysis, support vector machine

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Authors: R. Sabre, W. Horrigue, J. C. Simon

Abstract:

This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: spectral density, stable processes, aliasing, periodogram

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Authors: Rakesh Kumar Soni

Abstract:

Under free living conditions, human biological clocks show a periodicity of 24 hour for numerous physiological, behavioral and biochemical variables. However, this period is not the original period; rather it merely exhibits synchronization with the solar clock. It is, therefore, most important to investigate characteristics of human circadian clock, essentially in shift workers, who normally confront with contrasting social clocks. Aim of the present study was to investigate rest-activity rhythm and to vouch for the best technique for the computation of periods in this rhythm in subjects randomly selected from different groups of shift workers. The rest-activity rhythm was studied in forty-eight shift workers from three different organizations, namely Newspaper Printing Press (NPP), Chhattisgarh State Electricity Board (CSEB) and Raipur Alloys (RA). Shift workers of NPP (N = 20) were working on a permanent night shift schedule (NS; 20:00-04:00). However, in CSEB (N = 14) and RA (N = 14), shift workers were working in a 3-shift system comprising of rotations from night (NS; 22:00-06:00) to afternoon (AS; 14:00-22:00) and to morning shift (MS; 06:00-14:00). Each subject wore an Actiwatch (AW64, Mini Mitter Co. Inc., USA) for 7 and/or 21 consecutive days, only after furnishing a certificate of consent. One-minute epoch length was chosen for the collection of wrist activity data. Period was determined by using Actiware sleep software (Periodogram), Lomb-Scargle Periodogram (LSP) and Spectral analysis software (Spectre). Other statistical techniques, such as ANOVA and Duncan’s multiple-range test were also used whenever required. A statistically significant circadian rhythm in rest-activity, gauged by cosinor, was documented in all shift workers, irrespective of shift work. Results indicate that the efficiency of the technique to determine the period (τ) depended upon the clipping limits of the τs. It appears that the technique of spectre is more reliable.

Keywords: biological clock, rest activity rhythm, spectre, periodogram

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Authors: Karima Kimouche

Abstract:

In this paper, we consider the asymptotic problems in spectral analysis of stationary causal random fields. We impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear random fields. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given.

Keywords: spatial nonlinear processes, spectral estimators, GMC condition, bootstrap method

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

Abstract:

Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: Zavkiddin Mirtoshev, Mirabbos Mirkamalov

Abstract:

We have analyzed the time series of full disk integrated soft X-ray (SXR) and hard X-ray (HXR) emission from the solar corona during 2004 January 1 to 2009 December 31, covering the descending phase of solar cycle 23. We employed the daily X-ray index (DXI) derived from X-ray observations from the Solar X-ray Spectrometer (SOXS) mission in four different energy bands: 4-5.5; 5.5-7.5 keV (SXR) and 15-20; 20-25 keV (HXR). The application of Lomb-Scargle periodogram technique to the DXI time series observed by the Silicium detector in the energy bands reveals several short and intermediate periodicities of the X-ray corona. The DXI explicitly show the periods of 13.6 days, 26.7 days, 128.5 days, 151 days, 180 days, 220 days, 270 days, 1.24 year and 1.54 year periods in SXR as well as in HXR energy bands. Although all periods are above 70% confidence level in all energy bands, they show strong power in HXR emission in comparison to SXR emission. These periods are distinctly clear in three bands but somehow not unambiguously clear in 5.5-7.5 keV band. This might be due to the presence of Ferrum and Ferrum/Niccolum line features, which frequently vary with small scale flares like micro-flares. The regular 27-day rotation and 13.5 day period of sunspots from the invisible side of the Sun are found stronger in HXR band relative to SXR band. However, flare activity Rieger periods (150 and 180 days) and near Rieger period 220 days are very strong in HXR emission which is very much expected. On the other hand, our current study reveals strong 270 day periodicity in SXR emission which may be connected with tachocline, similar to a fundamental rotation period of the Sun. The 1.24 year and 1.54 year periodicities, represented from the present research work, are well observable in both SXR as well as in HXR channels. These long-term periodicities must also have connection with tachocline and should be regarded as a consequence of variation in rotational modulation over long time scales. The 1.24 year and 1.54 year periods are also found great importance and significance in the life formation and it evolution on the Earth, and therefore they also have great astro-biological importance. We gratefully acknowledge support by the Indian Centre for Space Science and Technology Education in Asia and the Pacific (CSSTEAP, the Centre is affiliated to the United Nations), Physical Research Laboratory (PRL) at Ahmedabad, India. This work has done under the supervision of Prof. Rajmal Jain and paper consist materials of pilot project and research part of the M. Tech program which was made during Space and Atmospheric Science Course.

Keywords: corona, flares, solar activity, X-ray emission

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