In this paper, the Zadeh method for the time-varying filtering of the non-stationary radar signal, embedded in non-Gaussian disturbances, has been considered analytically and numerically. The non-stationary radar signal has been received from a real radar receiver and only a real realisation has been accessible for experiments. The additive noise signal with Weibull distribution, as an example of non-Gaussian disturbances, has been taken into account. The linear, time-varying (LTV) Zadeh filter, for suppressing the noise signal and passing the radar signal, has been developed based on the concept of the Weyl symbol. The Weyl symbol, or equivalently the indicator function, has been designed from the Short Time Fourier Transform (STFT) as the time-frequency (TF) representation of a noisy signal. Comprehensive numerical experiments illustrate the results of the filtering process.
Polynomial Wigner Ville distribution (PWVD) is considered as a tool for recognition of signals with an unknown frequency modulation law. This time-frequency distribution (TF) with multi-linear kernel is an optimal form for signals with a polynomial frequency modulation law. Instantaneous frequency (IF) is the important property of non-stationary signals, i.e. signals whose spectral contents vary with time. Then the recognition of unknown signals can be formulated as the problem of estimation of its instantaneous frequency. The studies of estimation of IF for noiseless signals can be found in literature. The noise embedded in a signal has large influence on time-frequency distribution and can change the true value of the IF. Time-frequency distribution strongly depends on the kind of noise. In this paper signals embedded in additive gaussian and impulse noise have been considered. Estimation of the instantaneous fiequency in impulsive noise background is different than in gaussian noise and requires robust forms of time-frequency distributions. In this paper the application of the robust form of the Wigner-Ville distribution (WVD_r) and the robust form of the polynomial Wigner-Ville distribution (PWVD_r) for IF estimation is presented. Maxima of these distributions are assumed as the estimates of true values of IF. The theoretical background of WVD_r and PWVD_r distributions is introduced and several numerical experiments of IF estimation are presented.
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