Introduction to fractional linear systems. Part 2: Discrete-time case

Abstract

In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be considered as having fractional poles or zeros. The concept of fractional differaccumulation is discussed, gencralising the notions of fractal and lif noise, and introducing two kinds of fractional differaccumulated stochastic proccss: hyperbolic, resulting from fractional accumulation (similar to the continuous-time casc), and parabolic noise, resulting from fractional differencing.