Study Of Signal Measuring Based On Chaos Theory

It is an important content in modern information theory to detect weaksignal from the noise background. It is the method to utilize electronics,information theory and physics that analyses principle and law that the noiseproduces. Characteristic of weak signal is been studied and weak signal canbeen measured from noise. Studying principle and method that can be used tomeasure weak signal from noise is a comprehensive technology and mostadvanced field in technology. It is a kind of detection method in exploring touse nonlinear chaos oscillator for measuring weak signal. We can use thistechnology to measure the weak substance (such as weak light, smalldisplacement, little vibration) that the traditional idea think not can bemeasured, and precision of measuring weak signal is improved on the earth.There are a lot of methods that measuring weak signal, each one has itscharacteristic and range of application. According to the way of signalprocessing, it can be divided into two methods: one is time-domain method, theother is frequency-domain method. Time-domain method is simple, ocular,obvious physics and easy to be realize with hardware. The weak signalmeasuring method based on chaos theory which is introduced in this paper istime-domain method too.The measuring of the signal of the weak sine is important in numerousweak signal measuring methods. Since Fourier progression and Fouriertransform came out at the end of the 19th century, people have paid greatattention to sine signal measuring. It is made to be one of key problems ofsignal processing. Because of its particularity, sine signal, it is a measuretheory and research of method for great theory meaning to sine signal to make.And in fact, it is still extensively applied in the radar, sonar, vibration, thetrouble diagnosed, communication, physics, biomedicine and systemdistinguished. The recent studying shows that it is the foundation of robotdesign and great flexible structure control. Besides in signal processing, it isone of standards which are weighing resolution ratio and measure sensitivity ofalgorithm. The weak signal measuring method based on chaos oscillator which isintroduced in this paper is a new research direction of rising in recent years.This method uses chaos theory and differential equation theory in nonlinearscience in theory. In application, this method has wide prospect, it is hopeful toreduce equipment cost, simplify theory. Duffing oscillator of nonlineardynamic system is also studied in this paper. The main task of this paper is that using nonlinear chaos oscillator tomeasure weak sine signal from noise and the method of measuring sine signalwith unknown phase will be discussed too. In this paper, the contents whichwill be discussed is displayed: A. Utilize Melnikov method to judge whether the system enter the chaos state We observe phase portrait change or not through our naked eye, so theresult will unavoidably be influenced by subjective factor. Furthermore there isa question about simulating time. If time is short, the result is likely to be false.If time is long, working efficiency is too low. To solve this question, we utilizeMelnikov method to judge whether the system of Duffing oscillator equationenter the chaos state. The Melnikov method is detailed introduced in this paper.B. Discuss the principle of the chaos method to measure weak sinesignal and make lots simulating experiments Chaos system perturbation and sensitive to system parameter will makesystematic cycle result change. We utilize the principle to measure weak signal.The method is that the signal which will be measured acts as cycle perturbationof chaos system. Noise though strong, change of the system scarcely influences,once there is specific weak signal, because of the chaos system being sensitiveto sine signal, even little amplitude can make system change essentially. In thispaper, the phase portrait change from chaos to big yardstick cycle that is madeto be the judgment whether signals input. When the weak signal (amplitude isfor a , same frequency as system) joins the system which is on critical state,systematic amplitude at this moment turns into γd + a + n(t) and systematicphase portrait turns from critical state originally into yardstick cycle state. Thenwe regulate(minish)value γ. When γis equal toγ0 , phase portrait turns intocritical state again. It can be concluded that γ0 + a is equal toγd . It also canbe concluded that a is equal to γd ?γ0 .So we can make the conclusion thatthe weak signal is measured. Through lots simulating experiments we can draw the conclusion thatmeasuring minimum SNR door limit is-92.49dB. At present, other methods oftime-domain signal measuring do not have this precision. The minimum SNRdoor limit of other methods is only?10dB . So we can draw the conclusion that we can measure weak sine signalbased on chaos principle from noise background. C. Utilize equation group to measure weak sine signal with unknown...