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An evaluation of time frequency signals variation by using of the redundant wavelet transform

Keywords:

S.E. Stepanov – Ph. D. (Phys-Math.), Associate Professor, Bauman Moscow State Technical University, Kaluga Branch
M.A. Goroshko – Ph. D. (Phys-Math.), Associate Professor, Bauman Moscow State Technical University, Kaluga Branch


During the development of automatic control systems there are many cases when we need to solve the problem of processing time frequency signals. The solution is to be more complicated if the characteristics of noise can change during the time of system functioning. In some cases the fixing of the moment when such changes start is the main problem. In addition, the increasing complexity of technical systems require the creation of algorithms of processing of non-periodic signals that will have computational complexity, allowing their use in the real time. The paper presents an algorithm for solving the problem by pre-filtering of the measured values on the basis of a trous wavelet transform, which can be described as follows. Each time you receive a new measurement of the output signal the algorithm performs the following steps: 1. The wavelet transform of updated signal. 2. Hard thresholding new wavelet coefficients. 3. The inverse wavelet transform of the current signal measurement. 4. Isolation of measurement noise by finding the difference between the measured current value of the signal and the result of inverse wavelet transform. 5. Calculation of the unbiased estimate of the noise variance measured on a sample which consist of the last obtained values of measurement noise. 6. Using the new values of the estimate of the noise variance measurements to find the parameter estimates. The simulation results show that the algorithm can significantly improve the quality of the signal processing in the Kalman filter as a one-dimensional and multidimensional case. Analysis of the wavelet coefficients of the upper level signal decomposition provides the ability to capture the moment of increasing the intensity or amplitude of noise on the useful frequency signal that can be used in a variety of automatic control systems.
References:

  1. Olivier Renaud, Jean-Luc Starck, Fionn Murtagh. Kalman-type filtering using the Wavelet Transform.  http://citeseer.ist.psu.edu/598161.html, http://www.unige.ch/fapse/PSY/persons/prof-ana/renaud/papers/KalmanWavelet.pdf.
  2. Kravchenko V.F., Rvachev V.L. Algebra logiki, atomarny'e funkczii i vejvlety' v fizicheskix prilozheniyax. M.: FIZMATLIT. 2006.
  3. Vasil'ev V.N., Gurov I.P. Komp'yuternaya obrabotka signalov v prilozhenii k interferometricheskim sistemam. SPb: BXV – Sankt-Peterburg. 1998.
  4. Metody' klassicheskoj i sovremennoj teorii avtomaticheskogo upravleniya: Uchebnik v 5 tomax; T. 2: Statisticheskaya dinamika i identifikacziya sistem avtomaticheskogo upravleniya / Pod red. K.A.Pupkova, N.D. Egupova. M.: Izdatel'stvo MGTU im. N.E'. Baumana. 2004.

June 24, 2020
May 29, 2020

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