On Digital Realizations of Non-integer Order Filters

Abstract

Typical approach to non-integer order filtering consists of analogue design and implementation. Digital realization of non-integer order systems is susceptible to problems such as infinite memory requirement and sensitivity to numerical errors. The aim of this paper is to present two efficient methods for digital realization of noninteger order filters: discrete time-domain Oustaloup approximation and Laguerre impulse response approximation. Properties of both methods are investigated with use of non-integer low-pass filter. Filters realized with presented methods are then used for filtering of EEG signal. Paper concludes with discussion of merits and flaws of both methods.Keywords Non-integer order filter · Fractional filter · Oustaloup method · discretization · Laguerre impulse response approximation Work realized in the scope of project titled "Design and application of non-integer order subsystems in control systems". Project was financed by National Science Centre on the base of decision no.

Early-Stage Pilot Study on Using Fractional-Order Calculus-Based Filtering for the Purpose of Analysis of Electroencephalography Signals

“…The problem of approximating the non-integer order system with an integer order has been analyzed for many years and the most popular approaches are based on Oustaloup transfer function approximation. However, the problem with using the Oustaloup method is that it is very sensitive to high discretization frequencies and rounding errors and can become unstable easily (Baranowski et al, 2016).…”

“…The implementation of BFF Filtering is not very popular yet, but the authors assume that it will become widely used in the near future due to its efficiency and wider potential in development of frequency filter characteristics. The proposed method also offers more flexible adjustment of frequency characteristics (Baranowski et al, 2016). The previous applied methods have also been presented in studies conducted by Kawala-Janik et al (2014 in more detail.…”

Comparison of Smoothing Filters in Analysis of EEG Data for the Medical Diagnostics Purposes

“…The choice of appropriate filtering is challenging as non-linear filters differ from linear filters, in a way that they could be adaptive. In practice, this means that they retain the so-called edges, which are frequently present in the EEG signals [36][37][38]40,41]. Smoothing filters' (Savitzky-Golay and Median filters) application enables to correct inter alia spikes present in the data [25,27].…”

Convergence of Laguerre Impulse Response Approximation for Noninteger Order Systems

“…Our focus was mostly on generalizations of second-order filters developed by Radwan et al [27]. Detailed analysis of method operation was presented in [24].…”

“…Most applications of the method can be found in filtering and parametric optimization [21][22][23]. In [24], it was shown that in certain cases and at low orders of approximation LIRA outperforms Oustaloup method.…”