Least Lp-norm impulsive noise cancellation with polynomial filters

Parameter Estimation of Fractional Low Order Time-frequency Autoregressive Based on Infinite Variance Analysis

“…The larger error is produced if the AR model based on Gaussian is used in α stable distribution environment, therefore, the AR S Sα parameter estimation is proposed based on the fractional lower order moment (FLOM) in the literature [9,10], and the corresponding α spectrum estimation which can realize the frequency spectrum estimation *Address correspondence to this author at the Northeast Petroleum University, Daqing, Heilongjiang 066004, China; Tel: 13333305201; E-mail: Caoying0909@163.com under α stable distribution environment is proposed. The new improved AR model and ARMA model are put forward using the fractional lower order covariance (FLOC) replace FLOM in [11,12], realize the frequency spectrum estimation of the higher precision and resolution.…”

“…The α spectrum estimation only can realize the frequency estimation of the stationary S Sα process, and in view of the time-varying non-stationary process, TFAR nonstationary Gaussian excitation linear AR model method in literature [9][10][11][12] will no longer be applicable, hence, traditional Cohen class time-frequency distribution is improved based on the fractional lower order moment, a fractional lower order Cohen class time-frequency distribution is got [13,14], use fractional low-order covariance to replace correlation in the model, and put forward the non-stationary process fractional lower order time-frequency autoregressive (FLO-TFAR) model, the generalized TF-Yule-Walker equation is defined to compute the parameter estimation of the FLO-TFAR model. The FLO-TFAR model time-frequency spectrum estimation is defined, it can realize model timefrequency distribution of the observation signals.…”

Nonlinear Least lp-Norm Filters for Nonlinear Autoregressive α-Stable Processes

“…Since Mandelbrot's work on financial time series analysis [29], α-stable distributions have found applications in econometrics, telecommunications (e.g., [30]), radar signal processing (e.g., [49]), teletraffic analysis (e.g., [14]), audio restoration (e.g., [25]), and recently in image processing (e.g., [26]). In particular, linear parametric models with SαS innovations have been extensively studied [6,35].…”

“…Their analysis based on autocorrelation functions indicated underlying nonlinear characteristics for such data. Moreover, it was shown by Kuruoǧlu et al [25] that the minimum dispersion sense [35] optimal estimators are not necessarily linear and that there is a significant performance difference between the optimal linear estimator and the optimal Volterra type estimator which is a simple nonlinear estimator. Resnick suggests the bilinear model as a possible nonlinear model with α-stable innovations [38] but does not provide any estimation techniques for the model.…”

Noise suppression by removing singularities

“…Statistical filtering techniques include the L-estimators [16], [19], [26], the M-estimators [10], [9], and the more recent techniques based on higher order statistics [20], [22], [25]. The Fourier domain methods are based on the extraction of regularity by imposing some growth conditions on the signal, which reduces the space of admissible solutions to functions of given type and order, e.g., entire functions of exponential type [8], [21], [28], functions of polynomial growth [2], [11], [15], etc. In these methods, regularity is defined in a global sense based on Riemann's lemma (see [13, pp.…”