Weak Harmonic Signal Research Articles

Forced oscillation modes in a birhythmic system of two coupled relaxation oscillators near Andronoy - Hopf bifurcation

A system of two identical relaxation oscillators of the FitzZHugh-Nagumo type with the parameters chosen in the vicinity of a bifurcation of limit cycle emergence was examined for the dynamic modes arising in the presence of a weak harmonic signal applied to both elements. Slow variable exchange between them gives rise to three stable limit cycles called in-phase, anti-phase, and extremely asymmetrical, in which only one of the oscillators generates spikes. In this study, we show that slow variable exchange also causes this system to respond to weak harmonic forcing in a manner quite different from what is known in the classical dynamics of forced oscillations. In addition to the expected synchronization tongues generated by interaction of the signal with the in-phase attractor, we observed at least three other consequences of the coexistence of different solutions: (i) there appeared broad bands of synchronization of the signal with the anti-phase solution at high frequencies multiple to the frequency of the anti-phase oscillations, whereas the base synchronization frequency band became much narrower; (ii) signal period ranges were found in which the limit cycles were such that several spikes were produced over the complete period and each oscillator was characterized with the same set of discrete

Simulation and theoretical analysis on detection of the frequency of weak harmonic signals based on a special chaotic system

In order to study a kind of chaotic system which is based on the special Duffing-Homes equation, and use it to detect the unknown frequency of weak harmonious s ignals, we prove the existence of the periodic solution and the exclusivism of the solution, carry out simulation experiments to detect harmonious frequency us ing the periodic trajectory of a stable phase state.We also compute the detectio n error |Δω|,when the damping ratio (α) changes and the frequency changes fro m 1Hz to 200Hz. The results show that we have to choose the value of α correspo nding to the different range of frequency by simulation experiments.

Physical mechanism of the chaotic detection of the unknown frequency of weak harmonic signal and effects of damping ratio on the detection results

In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing–Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point (x, ) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio α.

Rejection properties of stochastic-resonance-based detectors of weak harmonic signals.

In [Phys. Rev. E 57, 6470 (1998)]] a thorough characterization in terms of receiver operating characteristics of stochastic-resonance detectors of weak harmonic signals of known frequency in additive Gaussian noise was given. It was shown that strobed sign-counting based strategies can be used to achieve a nice trade-off between performance and cost, by comparison with noncoherent correlators. Here we discuss the more realistic case where besides the sought signal (whose frequency is assumed known) further unwanted spectrally nearby signals with comparable amplitude are present. Rejection properties are discussed in terms of suitably defined false-alarm and false-dismissal probabilities for various values of interfering signal(s) strength and spectral separation.

Real-time second-harmonic-generation microscopy based on a 2-GHz repetition rate Ti:sapphire laser

The problem of weak harmonic generation signal intensity limited by photodamage probability in optical microscopy and spectroscopy could be resolved by increasing the repetition rate of the excitation light source. Here we demonstrate the first photomultiplier-based real-time second-harmonic-generation microscopy taking advantage of the strongly enhanced nonlinear signal from a high-repetition-rate Ti:sapphire laser. We also demonstrate that the photodamage possibility in common biological tissues can be efficiently reduced with this high repetition rate laser at a much higher average power level compared to the commonly used ~80- MHz repetition rate lasers.

Extracting Weak Harmonic Signals from Strong Chaotic Interference

A new method of extracting weak harmonic signals from chaotic interference is described in this paper. In this method, the received time series is assumed to be composed of some kind of an unknown chaotic signal and very weak harmonics. Thus, the local-geometric-projection method of noise reduction for a chaotic signal can be applied, and, as a result, the purified chaotic signal and the residual error sequences are obtained. The residual error sequences contain most of the weak signals and are modeled as an autoregressive moving average process, and frequencies of the harmonics are resolved. The principles of the approach and the algorithm employed are described in detail. The optimal selection of the algorithm parameters such as the length of the received data, the embedding dimension, and the number of nearest-neighbor points are also discussed. Some simulations of extracting the weak signals with various amplitudes and frequencies from strong chaotic interference are made. Excellent results are achieved from these computer simulations indicating the high effectiveness of the approach.

Coherence and stochastic resonance in a two-state system

The subject of our study is a two-state dynamics driven by Gaussian white noise and a weak harmonic signal. The system resulting from a piecewise linear FizHugh-Nagumo model in the case of perfect time scale separation between fast and slow variables shows either bistable, excitable, or oscillatory behavior. Its output spectra as well as the spectral power amplification of the signal can be calculated for arbitrary noise strength and frequency, allowing characterization of the coherence resonance in the bistable and excitable regimes as well as quantification of nonadiabatic resonances with respect to the external signal in all regimes.

A smectic liquid crystal containing three aromatic units which can be deposited by the LB method

We have synthesised a fumarate ester containing three aromatic rings and studied its properties in the bulk by DSC and other techniques. We have also deposited films of this compound by the LB method and by thermal evaporation in vacuo and characterised multilayers of it by low angle X-ray diffraction. DSC results show that the compound has a crystal to liquid crystal transition at 80°C and a liquid crystal to liquid transition at about 150°C. We have been able to photo-polymerise it while it is in the smectic state. Newly deposited multilayers exhibit clear X-ray diffractograms. However, if the multilayers are annealed at a temperature within the liquid crystalline region, the diffractograms become more clearly defined and the Bragg peaks increase in amplitude indicating an improvement in the coherence length in the direction normal to the plane. We have succeeded in depositing alternate layers of this compound and another compound having liquid crystal properties which we have previously studied. These have been exposed to radiation having a wavelength of 1.064 μm in an attempt to generate the second harmonic but without success. In view of the structure of the compound which has a series of ester bonds, each having an electric dipole moment, we assume that the conformation of the compound is such that these dipoles do not reinforce each others influence as otherwise we would have expected to have observed at least a weak second harmonic signal. Cast films of the compound heavily diluted with an inactive polymer and poled do show some SHG properties.

Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise

A thorough evaluation of stochastic resonance in the framework of statistical detection theory is presented both as a nonlinear signal preprocessor and as a detector. The pertinent receiver operating characteristics are compared with those of the known statistically optimum detector using extensive Monte Carlo simulations. Parameter optimization and computational budget aspects are discussed.

The search for weak harmonic signals in a spectrum with application to gravity data

When considering the search for discovery or amplitude estimation of a spectral line with a probabilistic approach, great attention must be paid to the meaning of each step. We give the probability law for the amplitude of a spectral peak in the presence of random noise appearing in a periodogram and discuss the effective probability of the existence of the corresponding wave. We find that the estimated amplitude of a spectral peak is biased and should be corrected when the signal-to-noise ratio is small. As a first application to gravity data, it results in a re-estimation of the gravimetric amplitude factors (delta factors) provided by least-squares tidal analysis. We also estimate the probability of observing a spectral line above a given level in the spectrum of a purely random noise. This allows us to compute for given spectrum the number of peaks expected to overcross the classical levels used in statistical analysis (like nσ, where σ is the standard deviation of the temporal noise distribution and n is an integer with typical values equal to 2 or 3). A specific application to real data is investigating the gravity spectrum derived from a 5 year record of the French superconducting gravimeter and we show that the predicted statistics are indeed in agreement with the observations. We also show the statistical consequence of using longer observing periods to obtain the spectral estimations. The problem of detecting translational motion of the Earth's solid inner core (Slichter modes) in a gravity spectrum is analyzed and the probabilities of having a triplet of random peaks thresholding specific levels in a given frequency window are computed. We show that, in the case of a typical gravity spectrum (1 year of hourly data and a frequency window of 0.03 cycle h −1), the probability of having a random set of three peaks exceeding a level of 3 σ, is very high. This emphasizes the need for a very careful analysis of spectral lines before inferring the existence of a true physical signal.

A search for the Slichter triplet in superconducting gravimeter data

There have been several investigations in the past for weak harmonic signals in the residual spectrum of superconducting gravimeter (SG) data. Recently, a stack of four European SG records led to the claim of the detection of the Slichter mode of translation of the inner core (Smylie, Science, 1992, 255: 1678–1682). We attempt to verify the presence of the Slichter triplet by two methods. We re-analyse the four European SG records with a spectral method differing from that used by Smylie et al. (Phys. Earth Planet. Inter., 1993, 80: 135–157) and compare the results to two homogeneous 2 year data sets from the French and Canadian SG. We find three weak peaks in the European stack coincident with the claimed triplet using a product spectrum, but these disappear when a cross spectrum is used which takes into account phase information. Further we find no evidence of the triplet in the 2 year data sets, where the noise level in the core-mode band is one order of magnitude lower than in the European stack. Moreover various synthetic tests (e.g. pure harmonics in random white noise; damped harmonics in brown noise) lead to the conclusion that a simulated Slichter triplet with characteristics similar to that claimed, would be easily detectable in our less noisy data, especially in cross spectral estimates.

Noise limitations in the core-mode band of superconducting gravimeter data

In recent years, several claims of detection of weak harmonic signals in the sub-tidal band of frequencies of high-quality gravimeter data have been made. Here, we review our attempts at confirming Smylie's claim of detection of the Slichter mode of inner-core oscillation using the same four data sets he and his colleagues used. We further examine the homogeneous 2 year data sets obtained from the superconducting gravimeters sited in Strasbourg and at Cantley, Quebec. We show that the power spectra of tidal-reduced, pressure and slew-corrected gravity residuals from these data are indistinguishable from a random walk process except in narrow bands dominated by residual earth tides and by harmonics of the diurnal thermal-atmospheric tide. Such a random ‘brown’ residual could result from mechanical instabilities and electronic noise in the instruments themselves, from site-specific tectonic noise, from local hydrological variations and pier instabilities or it could derive from unaccounted for variability in the atmospheric pressure in the vicinity of the instruments. We argue that the homogeneous 2 year data sets show no evidence whatever of Slichter harmonics even though our preprocessing methods reduce ‘apparent noise levels’ in the core-mode band by almost an order magnitude in comparison with the four data sets originally employed by Smylie et al. and, in their first attempted confirmation of his claimed discovery, by Jensen et al.

Induced supercontinuum and steepening of an ultrafast laser pulse

The problem of the propagation of an intense ultrashort pulse in a cubic (χ 3) nonlinear medium is generalized to include coupling between the primary and second harmonics signals. It is shown that the presence of a strong primary signal induces the superbroadening of the spectrum of a weak second harmonic signal and the deformation of its pulse shape.

Effect of lumped interference on a synchronized generator

Transients in a self-oscillator under biharmonic action are examined on the basis of an auto-parametric model of the synchronization phenomenon. It is shown that an external weak harmonic signal will influence the synchronization mode differently depending on the magnitude and detuning of the synchronizing emf.

Measurement System for Derivative Studies

A system for measuring I-V, dI/dV, and d2I/dV2 characteristics of two-terminal devices is described. An operational amplifier integrator is used to produce a sweep voltage. For derivative measurements the dc bias voltage is modulated by a constant ac voltage signal. Current is detected by a near-zero input impedance circuit with adjustable gain. A simple circuit utilizing an IGFET at zero drain voltage as a voltage controlled resistor compensates for harmonic content in the oscillator signal. It also enhances the detectability of weak harmonic signals in the presence of a strong fundamental signal by rejecting more than 90% of the strong signal. The system has been used to measure devices with impedances from a few ohms to over 105 Ω.