Periodic Detection Research Articles

A New Technique for the Detection of Periodic Signals in ``Colored'' Power Spectra

The light curves from a variety of celestial objects display aperiodic variations, often giving rise to red noise components in their power spectra. Searching for a narrow power spectrum peak resulting from a periodic modulation over the frequency range in which these "colored" noise components are dominant has proved a very complex task. Commonly used methods rely upon spectral smoothing or incoherent summation of sample spectra in order to decrease the variance of the power estimates. The consequent reduction in frequency resolution also causes a reduction of sensitivity to periodic signals. <P />We develop here a technique aimed at detecting periodicities in the presence of "colored" power spectrum components, while maintaining the highest Fourier frequency resolution. First, we introduce a simple approximation to the statistical properties of the "colored" power spectra from celestial objects, based on a few examples and the theory of linear processes. We then estimate the continuum components in the power spectrum through an ad hoc smoothing technique. This involves averaging the spectral estimates adjacent to each frequency over a suitably chosen interval in order to follow steep red noise features and produce estimates that are locally unaffected by the possible presence of a sharp peak. By dividing the sample spectrum by the smoothed one, a white noise-like spectrum is obtained, the approximate probability distribution of which is derived. A search for coherent pulsations is then carried out by looking for peaks in the divided spectrum, the chance probability of which is below a given detection threshold. If no significant peaks are found, an upper limit to the amplitude of a sinusoidal modulation is worked out for each searched frequency. <P />The technique is tested and its range of applicability determined through extensive numerical simulations. We present also an application to the X-ray light curves of V0332+53, a highly variable accreting X-ray pulsar, and GX 13+1, a bright and variable accreting source in the Galactic bulge.

The Soft and Medium-Energy X-Ray Variability of NGC 5548: A Reanalysis of EXOSAT Observations

view Abstract Citations (19) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Soft and Medium-Energy X-Ray Variability of NGC 5548: A Reanalysis of EXOSAT Observations Tagliaferri, G. ; Bao, G. ; Israel, G. L. ; Stella, L. ; Treves, A. Abstract We present a detailed cross-correlation (CCF) and power spectrum reanalysis of the X-ray light curves of the bright Seyfert 1 galaxy NGC 5548 obtained with EXOSAT. The 0.05-2 keV and 1-4 keV light curves are cross-correlated with the 1-9 keV and 4-9 keV light curves, respectively. We discuss how spurious time lags can be introduced by systematic effects related to detector swapping as well as the switching on and off of the instruments. We also find strong evidence that one of the ME detectors was not working normally during the second part of the 1986 March observation. When these effects are taken into account, the CCF peaks are in all cases consistent with the absence of delays between X-ray variations at different energies. This is unlike the results found by several authors based on the same data. The power spectra of the 1-9 keV light curves are calculated, and a detailed search for quasi-periodic oscillations (QPOs) is carried out on these spectra by using a new technique for the detection of periodic (or quasi-periodic) signals even in the presence of source noise variability. No significant peaks are found above the 95% confidence detection threshold, except during the second part of the 1986 March observation, most probably as a consequence of the ME detector malfunctioning. We discuss and compare our results with those published by Papadakis & Lawrence in 1993. Publication: The Astrophysical Journal Pub Date: July 1996 DOI: 10.1086/177411 arXiv: arXiv:astro-ph/9602073 Bibcode: 1996ApJ...465..181T Keywords: GALAXIES: INDIVIDUAL NGC NUMBER: NGC 5548; GALAXIES: SEYFERT; X-RAYS: GALAXIES; Astrophysics E-Print: 17 pages plus 11 postscript figures, uuencoded zipped file, PostScript. Accepted for publication in the Astrophysical Journal full text sources arXiv | ADS | data products SIMBAD (3) NED (1)

Stochastic Resonance in Chemistry. 1. The Belousov−Zhabotinsky Reaction

We demonstrate the phenomenon of stochastic resonance in a nonlinear chemical reaction. The term “stochastic resonance” (SR) denotes the detection of a weak periodic signal in a noisy system displaying a threshold. If the sum of the periodic signal and the noise amplitude crosses the threshold, an output pulse is triggered. At an optimal noise amplitude the distribution of pulse intervals as well as the signal-to-noise ratio will pass through a maximum. In the continuously stirred tank reactor (CSTR) experiments we superimpose a periodic flow rate signal on an excitable focal steady state located near a Hopf bifurcation in the Belousov−Zhabotinsky (BZ) reaction. In the Showalter−Noyes−Bar-Eli model of this reaction we vary the perturbation frequency and amplitude as well as the pulse length of the applied noise to elaborate the optimal conditions for stochastic resonance to occur in the model.

Detection of Weak Periodic Signals from Irregularly Spaced Observations

AbstractWe perform time series analysis on irregularly spaced data with large gaps. Our algorithm is based on multidimensional nonlinear optimisation. Particular emphasis is given to the selection and deletion of frequencies. The final result is checked by various statistical tests.

Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance.

In linear information theory, electrical engineering and neurobiology, random noise has traditionally been viewed as a detriment to information transmission. Stochastic resonance (SR) is a nonlinear, statistical dynamics whereby information flow in a multi-state system is enhanced by the presence of optimized, random noise. A major consequence of SR for signal reception is that it makes possible substantial improvements in the detection of weak periodic signals. Although SR has recently been demonstrated in several artificial physical systems, it may also occur naturally, and an intriguing possibility is that biological systems have evolved the capability to exploit SR by optimizing endogenous sources of noise. Sensory systems are an obvious place to look for SR, as they excel at detecting weak signals in a noisy environment. Here we demonstrate SR using external noise applied to crayfish mechanoreceptor cells. Our results show that individual neurons can provide a physiological substrate for SR in sensory systems.

Interrogation of a remote elliptical-core dual-mode fiber strain sensor by using a tandem interferometer configuration

We report on the interrogation of a lead-insensitive dual-mode fiber sensor using a white-light interferometric technique with a multimode laser-diode source. An elliptical-core dual-mode fiber acts as a remote-sensing interferometer, and a second dual-mode fiber acts as a receiver interferometer. We establish the sensor design for optimized performance and demonstrate the capability of accurate detection of periodic strain signals in the presence of, e.g., temperature-induced low-frequency phase drifts.

Probability of alarm detection in a search and rescue system

Diagnostic systems are often based on the detection of weak periodic signals buried in noise. As an illustrative example, a maritime search and rescue system is described. Here, alarms consist of frequency-modulated signals where the carrier frequency may vary in a certain range due to Doppler shifts. The signals are strongly corrupted by additive noise and by fading. For a given averaging time, the probability of missed alarms is computed and minimised, comparing different receiver structures and detection schemes. The theoretical investigations were verified in practical tests with striking accuracy.

Detection of periodic signals in noise: an iterative procedure

A method for detection and estimation of periodic signals in the presence of noise is described. The algorithm is an iterative improvement of the autoregressive-moving average estimation of a stochastic process and gives an exact frequency resolution of sinusoidal signals additively mixed with noise in a low signal-to-noise ratio only from a small number of measurements. The iterative improvement of the spectral estimation compared with other methods is demonstrated by examples.

Noncoherent detection of periodic signals

In this paper the optimal Bayes detector for a general periodic waveform having uniform delay and additive white Gaussian noise is examined. It is shown that the detector is much more complex than that for the we!l-known cases of pure sine waves (i.e., classical noncoherent detection)and narrow-hand signals. An interpretation of the optimal processor is presented, and several implementations are discussed.

On Transient and Periodic Signal Detection in Time-Varying Noise Power

Detectability of periodic and synchronously recurrent transient signals in a noisy environment in which the noise power is time varying is investigated. For at least one noise model, it is shown that the basic nonlinearity of the optimum detector is a limiter. Performance of this optimum detector is compared with analog cross-correlation and clipper cross-correlation (CCC) detectors. It is shown that the CCC performs nearly optimally, especially at low signal-to-noise ratios, and that its performance is significantly better than that of the analog cross correlator.

Correlation Entering New Fields with Real-Time Signal Analysis

Correlation analysis is a convenient technique for deyrtmining the spectral characteristics of a signal or the similarity of two different signals. One point of a correlation function is the long-term average of the product of two functions of time. The complete function is generated when the delay between the two time functions is varied. For example, if one voltage V1(t) and another voltage V2(t _ r), where r represents a finite and variable delay, are continuously multiplied together and the product fed into a low-pass filter, then the filter's output closely approximates the true mathematical correlation function. If V2; is identical to V1; in every respect except for the delay r, the result is the autocorrelation function. If V1; and V2; are totally different functions, then the result is the cross-correlation function. The outputs in both cases are functions of the delay time r. Mathematically for autocorrelation \begin{equation*}C_{11}(r) = \lim_{T\rightarrow\infty}\frac{1}{2T}\int^T_{-T}V_1(t)V_1(t - r) dt\end{equation*} for cross correlation \begin{equation*} C_{12}(r) = \lim_{T\rightarrow\infty}\frac{1}{2T}\int^T_{-T}V_1(t)V_2(t - r) dt \end{equation*} An instrument, therefore, that does this integrating process will show whether correlation exists between two signals and, if so, when maximum correlation takes place. In practice, the averaging process indicated in the above equations is performed only for a time longer than the longest period in signals f1(t) and f2(t). Autocorrelation is useful for the detection of an unknown periodic signal in the presence of noise or to measure some particular band of signal or noise frequencies.

"Application of Correlation Analysis to the Detection of Periodic Signals in Noise" [Comment, with replies

In the paper entitled "Application of correlation analysis to the detection of periodic signals in noise," by Y.W. Lee, T.P. Cheatham, Jr., and J.B. Wiesner (ibid., vol. 38, pp 1165-1171; Oct, 1950), several controvertible statements appeared. Because of the importance of this subject and the consequent possibility that the reader might easily arrive at erroneous conclusions, the commenting authors feel that these several statements should be amplified. In replying the original authors note the comments but fail to see that the statements concerned are incorrect or "controvertible." The commentors reply that they agree with the description of the special filter of North and Van Vleck and Middleton, but cannot follow the distinction which is made between this filter and a conventional filter in the penultimate paragraph of the reply. The original authors then note that these discussions primarily concern two statements of ours (as quoted in their reply) which Marchand, Leifer, and Holloway claim to be the "several controvertible statements" appearing in the paper. The validity of the first statement is not challenged after the reply. The original authors concludede, therefore, that it is not controvertible. With respect to the second statement, Marchand, Leifer, and Holloway do not disagree that the conventional filter described in the penultimate paragraph of our reply will theoretically achieve as much as a correlator in signal-to-noise ratio improvement. However, they do not follow the distinction between this filter and the North filter. The authors believe that the distinction between them has been made clear in their reply.

Application of Correlation Analysis to the Detection of Periodic Signals in Noise

The first part of this paper is a resume of correlation analysis. An interpretation of the correlation function of a continuous random process is given in terms of the sum of the products obtained by representing the process as a discrete time series. An electronic correlator capable of performing the necessary mathematical operations to obtain correlation functions is described. The theory of detection of a periodic signal in random noise by the correlation method and a description of the application of the correlator to the theory are presented.