### Browsing by Author "Astola, Jaakko"

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Item Generalized Hampel Filters(2016-12-01) Pearson, Ronald K.; Neuvo, Yrjö; Astola, Jaakko; Gabbouj, Moncef; Research Services; DataRobot; Tampere University of TechnologyThe standard median filter based on a symmetric moving window has only one tuning parameter: the window width. Despite this limitation, this filter has proven extremely useful and has motivated a number of extensions: weighted median filters, recursive median filters, and various cascade structures. The Hampel filter is a member of the class of decsion filters that replaces the central value in the data window with the median if it lies far enough from the median to be deemed an outlier. This filter depends on both the window width and an additional tuning parameter t, reducing to the median filter when t=0, so it may be regarded as another median filter extension. This paper adopts this view, defining and exploring the class of generalized Hampel filters obtained by applying the median filter extensions listed above: weighted Hampel filters, recursive Hampel filters, and their cascades. An important concept introduced here is that of an implosion sequence, a signal for which generalized Hampel filter performance is independent of the threshold parameter t. These sequences are important because the added flexibility of the generalized Hampel filters offers no practical advantage for implosion sequences. Partial characterization results are presented for these sequences, as are useful relationships between root sequences for generalized Hampel filters and their median-based counterparts. To illustrate the performance of this filter class, two examples are considered: one is simulation-based, providing a basis for quantitative evaluation of signal recovery performance as a function of t, while the other is a sequence of monthly Italian industrial production index values that exhibits glaring outliers.Item On two-dimensional polynomial predictors(2020) Astola, Jaakko; Neuvo, Yrjö; Rusu, Corneliu; Research Services; Tampere University; Technical University of Cluj-NapocaMany signals in nature and engineering systems can be locally modeled as relatively low degree polynomials, thus one-dimensional polynomial predictive filters are useful especially in time-critical systems. The goal of this paper is to introduce the two-dimensional polynomial predictive FIR filters and present few of their properties. First we discuss previous main results in one-dimensional polynomial predictive filters. Then we show how to find the coefficients and the system functions of the minimum area polynomial predictor, and we present the recursive form for the system function of a minimum area polynomial predictor. Finally, we approach the general form of 2D polynomial predictors.