By U.A.Bakshi, A.P.Godse
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Extra info for Analog And Digital Electronics
FfGn can be expressed as the sum of low and high frequency components as X i = X i(L) + X i(H ) (L) where, X i denotes the low frequency terms which is a weighted sum of Markov(H ) Gauss processes and X i denotes the high frequency terms which is a Markov-Gauss (L) process. 41). 4 Multiple Timescale Fluctuation Approach The weighted sum of the exponential function of the time lag leads to an approximation of the fGn autocorrelation function Eq. 39 on the basic time scale. An algorithm 42 3 Long Range Dependence, Stable Distributions and Self-Similarity to generate fGn can be derived using this property.
Signal Process. 86(10), 2505–2515 (2006). : An introduction to the fractional continuous-time linear systems: the 21st century systems. IEEE Circuits Syst. Mag. : On the fractional linear scale invariant systems. IEEE Trans. Signal Process. : Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. : Comparison between two approximation methods of state space fractional systems. Signal Process. 91(3), 461–469 (2011). : On fractional systems H< inf> ∞< /inf>,-Norm computation.
Also for H = 1/2, we have r x (l) = δ(l) which implies that the fGn process is white noise. 35) where C H = 2H (2H ) sin (π H ) is a constant. For H = 1/2, a flat Power Spectral Density (PSD) is obtained, which implies that for this special case the fGn process is actually white noise. e. asymptotically). 36) for large lags. e. 37) The fGn process has long memory in the range 1/2 < H < 1, since ∞ jω → ∞ as |ω| → 0. In this case l=−∞ r (l) = ∞ or equivalently R e the autocorrelation decays slowly and the frequency response is analogous to a low-pass filter.