Study On Weak Signal Detection Approaches Based On Chaotic Oscillator

1. IntroductionThe theory and the methods of study weak signal detection is compositivetechnology and cuspidate field of measurement technology under noise background.So we can detect very weak signal that can not be detected normally and themeasurement precision of weak signal can be raised. So it is the important methodof developing new technology to find new principal.It is important of weak sinusoidal signal in weak voltage signal detection field.Because of the structure of particularity of sinusoidal signal, it has an importantsignification in study of sinusoidal signal detection theory and method ,in fact ,butalso has application in radar,sonar,communication and biologic medicine field. Itcan be seen from current study that it is a base of robot design. Moreover in signalprocessing ,it is a standard of detection statoscope and scaling apparatus orresolation of arithmetic.Weak sinusoidal signal voltage measurement has all kinds of methods, it has twokinds. One is time-domain method and the other is frequency-domain method. Theexcellence of time-domain method are simple,intuitionistic,and can be realized byhardware. It has long history and broad application. The time-domain method makesuppose to signal and noise ahead of time. So the fact project can not be appliedexpediently.The current new weak signal detection method is combining chaotic theory withsignal detection. This project has all excellent of time-domain method, and it hadbetter than the time-domain method at capability. This project may reduceequipment cost, and predigest theory. So weak signal detection has widest appliedforeground.2. weak signal detection theory based on chaotic phrase change andsimulatorThe chaotic system is sensitive to small signal and immune to noise. The traitmake it potential of signal detection. The perturbation of parameter of non-lineardynamical system sometimes can result in change of periodic salvation ,detectionweak signal can use chaotic oscillator, so in fact detection of the measured signalcan be as perturbation of periodic driving of Duffing equation, noise is sostrong ,but it can not influence system state, and having special signal can changephrase , though its amplitude is so small, through system state, can detect clearlyspecifically signal .a conclusion is educed that the method of weak signal detectionbased on chaos theory is feasible and effective. The signal studied is measurecd signal of periodic frequency 1rad/s. put it intoDuffing equation , the effect is good. But in fact ,frequency of measured signal maynot be 1rad/s. we change Duffing equation ,and the Duffing equation changedmay measure every frequency measured signal , after the Duffing equationwas changed by the time scale Ï„. And state equation is as follows: computer simulator model of Duffing equation Homes typeafter so much simulation experiment. We can see that adjusted to adaptto a different frequency of measured signal. Experiment show: when added in Gauss-white noise ,the phrasetrajectory of system is still in chaotic state . so noise is so stronger,but stranger attractor still bondage phrase point in that trajectory,chaotic system is immune to noise. We studied the bifurcation of Duffing oscillator. Because of weakperturbation of parameter of chaotic system, system is from doubleperiodic bifurcation to chaos, when one double periodic bifurcationoccur, we can find a pair of frequency spectrum, frequency spectrum of perioddoubling bifurcation added continuously ,system came into chaotic state in end.The chaotic trait that arouse from period doubling bifurcation came from parameterperturbation of Duffing oscillator was studied at theory and computer simulationaccording to the trait of white noise and chaotic signal similar to the white noisesignal, Now, explain is as follows:1. the theory and simulation test that chaotic signal is non-periodic and its power spectrum is continuous broad band trait. Because of non-stable limit-cycle. Its spectrum has obvious peak in low frequency band. The power spectrum similar to noise is the trait of chaotic system.2. the collation of signal is important question of signal processing ,but we can not gave answer from theory. But begin with the chaotic study of form function, can see extreme sensitivity of initial condition, in fact, it declaration that chaotic series are most utter non-correlation (cross-correlation almost is zero).3. the sensitivity of initial value of chaotic vibration mean the missing the information in movement course,so,after some time,the auto-correlation go to zero. Detection signal used chaotic oscillator method based on input ofphase trajectory of chaotic system is chaotic state or stable periodicmotion state to detect signal. Because of the change of chaotic statephase trajectory to stable periodic motion,can only watch results byour eyes.so can influence by investigator, and sometime includingefficiency. We can set up a new chaotic criterion combining with Duffingequation. The minimum of ratio f k is named as chaotic threshold ,chaoticthreshold is having nothing with the the frequency of periodic driving,...