Fractional discrete-time signal processing: Scale conversion and linear prediction
Widening the concepts and results in fractional discrete-time linear prediction, a generalization is obtained. Using the Cauchy integrals, causal systems described by linear fractional difference equations are studied. In its eight sections, the paper presents the theory, a practical algorithm, simulations and conclusions as follows. In the first section the general problem is presented, and in the second one a fractional delay and lead concepts review takes place. In section 3 the scale change property is generalized and in section 4 the dual of the results is used to perform an interesting practical application, namely the zoom transform. Working in the context of a stationary real stochastic process, in section 5 fractional linear prediction is presented. In section 6, the previous results are generalized and a solution to an interesting problem from economics is proposed. Simulation results are given in the seventh section to illustrate the behaviour of the algorithm, and in the last section some conclusions about the topic are presented.
scientific article; zbMATH DE number 1850653