Modeling of fractional-order signals from their ramp cepstra

The bond between causal complex cepstra and Sheffer polynomials

“…For example, when the complex cepstrum of an exponential sequence is scaled by a fraction, the result is a fractional-order signal. Recently, a method was formulated for modeling fractional-order signals from their ramp cepstra [9]. Sheffer polynomial sets that exist in the mathematical literature can be utilized to generate signals that have more advanced singularities than poles.…”

“…Equation (6b) leads to (8) The function satisfies the conditions of (6). Setting to and finding the basic Sheffer polynomial set associated with transforms (8) into (9) from which follows (10)…”