Time-domain Oustaloup approximation

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

“…Figure 3 illustrates spectral analysis of the same signal (sample 1) as in Figure 2. It is possible to observe the damping of 28 dB/dec, which is not possible while using traditional filters (for further details please see: Baranowski et al, 2014aBaranowski et al, , 2014bPiatek et al, 2014). In Figure 4, the comparison of using two types of filtering -a basic band-pass (8 and 12 Hz) filter and a fractional BFF filter (with the given parameters: α = 0.7, b = 11.1688, c = 124.7412) -is presented.…”

“…For this paper, the fractional filtering process was carried out with the implementation of the Laguerre impulse response approximation (Baranowski et al, 2014a). Fractional-order differentiators and integrators contain very interesting features, which could be successfully applied for the purpose of design of digital filters -later applied for analysis of biomedical data (Ferdi, 2011).…”

On Digital Realizations of Non-integer Order Filters

“…The problem is that Oustaloup method is very sensitive to high discretization frequencies and rounding errors. It was observed in earlier authors' works [7] that it can become destabilized very easily. On the other hand, CFE method shows inferior quality in frequency characteristic representation [25].…”

“…Those first-order systems will be then collected in a single matrix resulting in full matrix realization. The results were first presented in authors' earlier works [7] and [6]. This approach proved to be more robust to different discretization schemes.…”

“…State-space realization of Oustaloup transfer function was considered in, e.g., [23,36,39,40]; however, its discrete properties were not considered in this context. In this paper, the method from [7] is used. This approach allows avoiding numerical problems observed in practical realization.…”