Weak Signal Detection And Estimation Based On Multi-wavelet Transform And Dufifng Oscillator

Weak signal detection and estimation has been a hotspot in the modern signal processingtechnology and has derived growing attention from numerous experts for its wide applicationin fields including biology, chemical industry, military industry, marine exploration, faultdiagnosis in power system, ect.The method of weak signal detection and estimation based on Duffing oscillator mainlyadopts the bifurcate of Duffing oscillator and the immunity of noise, that is, the Duffingoscillator being sensitive to periodic signals and immunity of noise, and the weak signaldetected and estimated through the difference of the input signal of Duffing oscillator’sdynamic behavior. But the ability of detecting and estimating of the oscillator will beweakened as the noise jamming aggravates. While multiwavelet transform, which bearsorthogonality, symmetry and short supportive in property, possess better de-noising effectthan wavelet transfer. This paper puts forward an algorithm, in which firstly the signals arede-noised by multiwavelet and then input into Duffing oscillator, to detect and estimate theweak signals based on multiwavelet transform and Duffing oscillator. This research covers:1. The matrix form of multiwavelet transform, which provides a clear way in mathematicalexpression of the multiwavelet transform, an easy way in data collection in each sub-bandand a time-saving way in calculation.2. An energy function-based multiwavelet local threshold de-nosing algorithm, which givesfull scopes to the advantages of creating several high frequency sub-bands in eachmultiwavelet transform, and offers an flexible way to assign the thresholds.3. A frequency detecting algorithm on weak signals based on multiwavelet transform andDuffing oscillators, in which weak signals are detected by imputing signals that have beende-noised by multiwave threshold into Duffing oscillators, and which is superior to chaosalgorithm in detection rate through simulation experiments.4. A frequency estimating algorithm on weak signals based on multiwavelet transform andDuffing oscillators, in which signals that have been de-noised by multiwave threshold areimput into Duffing sequence, and the frequency of weak signals are estimated throughintermittent chaos theory, which is superior to chaos algorithm in accuracy throughsimulation experiments. 5. An initial phase estimating algorithm based on signal delay, in which the signals that havebeen de-noised by multiwave threshold are delayed and then imput into Duffingoscillators, and the phase is estimated according to the difference in the dynamic behaviorof Duffing oscillators.