Discrete Autocorrelation Function Research Articles

Owens Valley Radio Observatory monitoring of LS I +61°303 completes three cycles of the super-orbital modulation

Context. The high-mass X-ray binary LS I +61°303 is composed of a Be-type star and a compact object in an eccentric orbit. The emission from this source is variable and periodic across the electromagnetic spectrum, from radio to very high-energy γ rays. The orbital period has been determined as P1 ≈ 26.5 d, and the source also features a super-orbital period with a value of Plong ≈ 4.6 years. Long-term monitoring of the binary by the Owens Valley Radio Observatory (OVRO) at 15 GHz has now completed 13.8 years, which corresponds to three full cycles of the super-orbital period. This is exactly one long-term cycle more than in the previous publication about OVRO observations of this source. Aims. Our aim is to investigate the presence and the stability of periodic signals in the radio data and to test if they are in agreement with previous results. This will contribute to the understanding of the physical processes behind the non-thermal emission from this source. Methods. We performed a timing analysis of the OVRO radio light curve and made use of the generalized Lomb-Scargle periodogram. We also combined the OVRO data with the full archive of previous radio observations and computed the discrete autocorrelation function. Results. The most powerful features in the periodogram of the OVRO data are two peaks at P1 = 26.49 ± 0.05 d and P2 = 26.93 ± 0.05 d, which are well separated from each other and clearly stand out above the very low noise level. The previously detected long-term period is still present in these new radio data, and our measurement is Plong = 1698 ± 196 d. Dividing the OVRO data into three segments of equal length showed that the two periods, P1 and P2, are present in the periodogram of each of the consecutive long-term cycles. Our analysis of the full radio archive resulted in the detection of the same three periods, and the autocorrelation function showed a regular pattern, proving the continuity of the decades-spanning stability of the super-orbital modulation. In addition, we report a possible systematic modulation of the radio flux density with a timescale of approximately 40 years that has so far remained unnoticed. Conclusions. The physical model of a relativistic jet whose mass loading is modulated with the orbital period P1 and is precessing with the slightly larger period P2, giving rise to a beating with period Plong, had previously been able to reproduce the radio and gigaelectron volt emission from this source. The ongoing presence and the stability of the periodic signals imply that this model is still the most plausible explanation for the physical processes at work in this source.

GPS First Path Detection Network Based on MLP-Mixers

BPSK modulated GPS L1 CA signal is the most widely used GNSS signal to date, and the first path detection (FPD) of the conventional GPS L1 CA signals is the most challenging problem to ensure reliable GPS positioning in multipath environments. In this paper, we propose an FPD network (FPDN) based on multi-layer perceptron (MLP)-Mixer to extract the first path from the discrete autocorrelation function (ACF) output accurately with low computational cost. In addition, the proposed FPDN is useful in practice because it is robust to noise and achieves a high FPD performance without any prior assumption on the number of total incoming multipath, which is required for conventional signal processing-based FPD techniques. We compare the performance of the proposed FPDN to that of diverse conventional techniques, such as techniques based on narrow correlator, super-resolution, and some widely used CNNs such as VGGNet, ResNet, and U-Net, through simulations and field tests. As demonstrated, the proposed FPDN outperforms all of the compared FPD techniques in terms of the computational cost and accuracy for wide range of carrier-to-noise (C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) ratios.

The theory of electrochemical noise in equilibrium state within the Einstein concept

• Autocorrelation analysis of electrochemical noise Brownian coordinate. • Fluctuation-dissipation relations for autocorrelations of Brownian coordinate. • Fluctuation-dissipation relations for structure function of Brownian coordinate. • Autocorrelations of Brownian coordinate of Voigt circuit noise. The theory of electrochemical noise is considered within the Einstein concept. Discrete fluctuation–dissipation relations for the Brownian coordinate of electrochemical potential noise are determined. It is shown that, in the equilibrium state, there is a linear relationship between the discrete autocorrelation function of the Brownian coordinate of electrochemical potential noise and the second order difference of macroscopic linear response of the electrochemical Brownian coordinate to the external action in the form of a single step of constant electric current. Using the discrete fluctuation–dissipation relations, the discrete autocorrelation function of the Brownian coordinate of equilibrium potential noise is calculated for the Voight electrochemical circuit, which contains the electric double layer capacitance and the electrochemical discharge resistance. In the direct experiment, it is shown that the intrinsic noise of the measuring instrument (based on the AD7176 evaluation board) does not hamper the measurement of the structure function of the Brownian coordinate of corrosion noise. The electrochemical noise diagnostics based on the Einstein concept is a promising supplement to the electrochemical noise diagnostics based on the Nyquist concept.

Blazar Mrk 501 shows rhythmic oscillations in its γ-ray emission

Quasi-periodic oscillations (QPO) originating from innermost regions of blazars can provide unique perspective of some of the burning issues in blazar studies including disk-jet connection, launch of relativistic jets from the central engine, and other extreme conditions near the fast rotating supermassive black holes. However, a number of hurdles associated with searching QPOs in blazars e.g., red-noise dominance, modest significance of the detection and periodic modulation lasting for only a couple of cycles, make it difficult to estimate the true significance of the detection. In this work, we report a $\sim$ 330-day QPO in the Fermi/LAT observations of the blazar Mrk 501 spanning nearly a decade. To establish consistency of the result, we adopted multiple approaches to the time series analysis and employed four widely known methods. Among these, Lomb-Scargle periodogram and weighted wavelet z-transform represent frequency domain based methods whereas epoch folding and z-transformed discrete auto-correlation function are time-domain based analysis. Power spectrum response method was followed to properly account for the red-noise, largely inherent in blazar light curves. Both local and global significance of the signal were found to be above 99\% over possible spurious detection. In the context where not many $\gamma$-ray QPOs have been reported to last more than 5 cycles, this might be one of the few instances where we witness a sub-year timescale $\gamma$-ray QPO persisting nearly 7 cycles. A number of possible scenarios linked with binary supermassive black hole, relativistic jets, and accretion disks can be invoked to explain the transient QPO.

Parametric Spectral Analysis of Noisy Signals with Unimodal Spectrum

The article proposes a method for the coefficients reconstruction of a discrete autocorrelation function of random signals with a unimodal power spectral density to construct their parametric models. The method is based on finding the optimal values of the relative width ΔFT and the weighting factor α in [0; 1] of the spectral mode, which characterizes the share of the Gaussian and resonant components in the spectrum envelope. The proposed method makes it possible to reduce by 1.5–4 times the discrepancy between the control and estimated spectra in comparison with the known approaches to parametric spectral analysis. An increase in the adequacy of spectral estimation makes it possible to reduce the length M of the analyzed time sample by a factor of 2.3–4 times, while maintaining the accuracy of the spectral analysis achieved by other known parametric methods. Winnings are achieved by using a priori information about the spectral properties of the analyzed process.

Detection of Periodic Radio Signal from the Blazar J1043+2408

The search for periodic signals from blazars has become a widely discussed topic in recent years. In the scenario that such periodic changes originate from the innermost regions of blazars, the signals bear imprints of the processes occurring near the central engine, which are mostly inaccessible to our direct view. Such signals provide insights into various aspect of blazar studies, including disk-jet connection, magnetic-field configuration and, more importantly, strong gravity near the supermassive black holes and release of gravitational waves from binary supermassive-black-hole systems. In this work, we report the detection of a periodic signal in the radio light curve of blazar J1043+2408 spanning ∼10.5 years. We performed multiple methods of time-series analysis, namely, epoch folding, Lomb–Scargle periodogram, and discrete autocorrelation function. All three methods consistently revealed a repeating signal with a periodicity of ∼560 days. To robustly account for the red-noise processes usually dominant in the blazar variability and other possible artefacts, a large number of Monte Carlo simulations were performed. This allowed us to estimate high significance (99.9% local and 99.4% global) against possible spurious detection. As possible explanations, we discuss a number of scenarios, including binary supermassive-black-hole systems, Lense–Thirring precession, and jet precession.

Analysis of noncommensurate sampling effects on the performance of PN code tracking loops

Noncoherent early-late processing (NELP) code tracking loops are often implemented using digital hardware for digital global positioning system (GPS) receivers. Noncommensurate sampling technology is widely used because it is viewed as an effective solution to cope with the drawback of digital effects. However, the relationship between the sampling rate and auto-correlation function (ACF) is not adequately characterized by traditional analysis. The principles for selecting the sampling rate are still not apparent. In order to solve this problem, we first analyzed the effects of different sampling rates on ACF and obtained the analytical form of a discrete auto-correlation function (DACF) for a noncommensurate sampling rate. Based on the result, the relationship between the step variation in DACF and NELP parameters such as sampling rate, integration time, and correlator spacing was determined. The maximum step variation size of DACF was also determined. However, considering the actual situation, additional factors such as code Doppler shift, precorrelation filter, and thermal noise may degrade the step variation of DACF. The relationship between the step variation and these factors was analyzed separately. An appropriate sampling rate and appropriate correlator spacing were proposed to achieve the typical accuracy of measurement. The numerical simulation verified the validity of the above theoretical analyses, and finally, the conclusions and design constraints for the digital GPS receiver are summarized.

A Search for Quasi-periodic Oscillations in the Blazar 1ES 1959+650

Abstract We have searched quasi-periodic oscillations (QPOs) in the 15 GHz light curve of the BL Lac object 1ES 1959+650 monitored by the Owens Valley Radio Observatory 40 m telescope during the period from 2008 January to 2016 February, using the Lomb–Scargle Periodogram, power spectral density (PSD), discrete autocorrelation function, and phase dispersion minimization (PDM) techniques. The red noise background has been established via the PSD method, and no QPO can be derived at the 3σ confidence level accounting for the impact of the red noise variability. We conclude that the light curve of 1ES 1959+650 can be explained by a stochastic red noise process that contributes greatly to the total observed variability amplitude, dominates the power spectrum, causes spurious bumps and wiggles in the autocorrelation function and can result in the variance of the folded light curve decreasing toward lower temporal frequencies when few-cycle, sinusoid-like patterns are present. Moreover, many early supposed periodicity claims for blazar light curves need to be reevaluated assuming red noise.

KEPLEROBSERVATIONS OF RAPID OPTICAL VARIABILITY IN THE BL LACERTAE OBJECT W2R1926+42

We present the first Kepler monitoring of a strongly variable BL Lac, W2R1926+42. The light curve covers 181 days with ~0.2% errors, 30 minute sampling and >90% duty cycle, showing numerous delta I/I > 25% flares over timescales as short as a day. The flux distribution is highly skewed and non-Gaussian. The variability shows a strong rms-flux correlation with the clearest evidence to date for non-linearity in this relation. We introduce a method to measure periodograms from the discrete autocorrelation function, an approach that may be well-suited to a wide range of Kepler data. The periodogram is not consistent with a simple power-law, but shows a flattening at frequencies below 7x10-5 Hz. Simple models of the power spectrum, such as a broken power law, do not produce acceptable fits, indicating that the Kepler blazar light curve requires more sophisticated mathematical and physical descriptions than currently in use.

Transiting exoplanets from the CoRoT space mission

CoRoT, the first space-based transit search, provides ultra-high precision light curves with continuous time-sampling over periods, of up to 5 months. This allows the detection of transiting planets with relatively long periods, and the simultaneous study of the host star's photometric variability. In this letter, we report on the discovery of the transiting giant planet CoRoT-Exo-4b and use the CoRoT light curve to perform a detailed analysis of the transit and to determine the stellar rotation period. The CoRoT light curve was pre-processed to remove outliers and correct for orbital residuals and artefacts due to hot pixels on the detector. After removing stellar variability around each transit, the transit light curve was analysed to determine the transit parameters. A discrete auto-correlation function method was used to derive the rotation period of the star from the out-of-transit light curve. We derive periods for the planet's orbit and star's rotation of 9.20205 +/- 0.00037 and 8.87 +/- 1.12 days respectively, consistent with a synchronised system. We also derive the inclination, i = 90.00 -0.085 +0.000 in degrees, the ratio of the orbital distance to the stellar radius, a/R_s = 17.36 -0.25 +0.05, and the planet to star radius ratio R_p/R_s = 0.1047 -0.0022 +0.0041. We discuss briefly the coincidence between the orbital period of the planet and the stellar rotation period and its possible implications for the system's migration and star-planet interaction history.

PERIODICITY ANALYSIS OF THE RADIO CURVE OF PKS 1510-089 AND IMPLICATIONS FOR ITS CENTRAL STRUCTURE

We have analyzed the radio light curves of PKS 1510-089 at 37 and 22 GHz from 1990 to 2005 taken from the database of the Metsahovi Radio Observatory, and find evidence of quasi-periodic outbursts. The light curves show great activity with very complicated non-sinusoidal variations. Using Jurkervich's method, the power spectrum method, and the discrete autocorrelation function to analyze these data, we have found two periods of p(1) = 0.92 +/- 0.04 yr and p(2) = 1.82 +/- 0.12 yr for the outbursts in PKS 1510-089. It is interesting to note that the results for two frequencies and three methods are almost the same and p(2) approximate to 2p(1). In addition, these results are in good agreement with the periodic deep flux minima of 1.84 +/- 0.1 yr ( half period similar to 0.92 +/- 0.03 yr) observed by us and other authors in the optical band in 2002, 2004, and 2005.

Total flux density radio observations as a tool for understanding AGN behaviour

A wealth of information on the properties of jets in Active Galactic Nuclei (AGNs) can be derived from total flux density observations at high radio frequencies. This includes, for example, the Doppler factor, the Lorentz factor, and the viewing angle of the jet. We have earlier calculated these parameters for a sample of ∼80 sources of different AGN types using almost 20 years of 22 and 37 GHz data from Metsahovi Radio Observatory. We have now gathered data for an additional ten years, and studied the long term characteristic variability time scales of a large sample of AGNs using the first order structure function, the discrete autocorrelation function and the Lomb-Scargle periodogram. Some of the results will be presented in this paper. We also stress the importance of long term observations of AGNs, the main reason for this being misinterpretations of source properties due to insufficient time coverage. Only a few observing epochs will too easily lead to incorrect conclusions about variability, continuum spectra, and the general detectability of the source, not to mention the exclusion of interesting objects from further studies. This is particularly important when considering, for example, the Planck satellite for which the quality of the main mission product, the accurate cosmic microwave background anisotropy maps, depends heavily on the elimination of foreground sources such as AGNs.

A search for periodicity in the light curves of selected blazars

We present an analysis of multifrequency light curves of the sources 2223-052 (3C 446), 2230+114 (CTA 102), and 2251+158 (3C 454.3), which had shown evidence of quasiperiodic activity. The analysis made use of data from the University of Michigan Radio Astronomy Observatory (USA) at 4.8, 8, and 14.5 GHz, as well as the Metsahovi Radio Astronomy Observatory (Finland) at 22 and 37 GHz. Application of two different methods (the discrete autocorrelation function and the method of Jurkevich) both revealed evidence for periodicity in the flux variations of these sources at essentially all frequencies. The periods derived for at least two of the sources—2223-052 and 2251+158—are in good agreement with the time interval between the appearance of successive VLBI components. The derived periods for 2251+158 (P = 12.4 yr and 2223-052 (P = 5.8 yr) coincide with the periods found earlier by other authors based on optical light curves.

Genetic search for Golomb arrays

Genetic search with a decision level chromosome is used to search efficiently for Golomb (1982) arrays. A Golomb array A is a binary array with three values for its discrete autocorrelation function; M, the number of ones in A for no offset, 1 when there is partial overlap, and 0 otherwise. In one dimension, A is known as a Golomb ruler. The method yields improvement because the genetic search considers only feasible solutions in the most likely portion of the search space. Each chromosome bit represents a decision to place a one in an iterative construction. The representation includes all possible arrays. Since the chromosome bits represent binary decisions in the search space, genetic operations (such as crossover and mutation) always result in feasible descendent chromosomes. Experimental results include comparison to previously known search methods and several new arrays. These results indicate that the proposed search is significantly more efficient than prior methods.

Chaotic Behavior of an Inelastic Beam

ABSTRACTThe dynamical system considered in this paper is an inelastic beam whose supports are subjected to a harmonic excitation. This paper first explores whether the system has chaotic motion. The appearance of the irregular time history, strange attractor on the Poincaré map as well as period-doubling bifurcation phenomenon strongly indicates that chaos indeed exist in this system. After finding the chaos phenomenon, this paper continues to investigate the relationship between the decay time of the autocorrelation function and the largest Lyapunov exponent. The Poincaré mapping points are chosen to be the sampled function of the discrete autocorrelation function. It's found that a power model of regression analysis can fit with good accuracy the data points, which are composed of the mapping times for the autocorrelation to decay into the square of the mean of the Poincaré points and the corresponding largest Lyapunov exponent.

The autocorrelation function of a pseudointegrable system

The autocorrelation function of a pseudointegrable system is considered. The system consists of “billiards” on plane surface formed out of three squares arranged in an “L” shape. This system has the important property of being constructed from copies of an integrable subsystem, the single square. The motion can be decomposed into a continuous and a discrete part, the unpredictability in the system being associated with the latter. A discrete autocorrelation function is calculated, and its decay properties investigated. Structure found in this autocorrelation function is associated with the continued fraction expansion of the ratio of velocity components. For repeating continued fractions, such as the golden mean, the autocorrelation function exhibits a selfsimilar structure. For the general case of a randomly chosen velocity ratio, we derive the time dependence of the number of occurences of “large” autocorrelation values, which differs from the behavior in integrable and chaotic systems.