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

Author

Ortigueira, M.D.

Author_Institution

Inst. Superior Tecnico, Lisbon, Portugal

Volume

147

Issue

1

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

71

Lastpage

78

Abstract

For pt.I see ibid., vol.147, no.1, p.62 (2000). 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 to 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 generalising the notions of fractal and 1/f noise, and introducing two kinds of fractional differaccumulated stochastic process: hyperbolic, resulting from fractional accumulation (similar to the continuous-time case), and parabolic noise, resulting from fractional differencing

Keywords

1/f noise; difference equations; discrete time systems; fractals; frequency response; hyperbolic equations; linear systems; parabolic equations; poles and zeros; signal processing; stochastic processes; transfer functions; transient response; 1/f noise; discrete linear systems; discrete-time fractional linear systems; fractal noise; fractal signals; fractional differaccumulation; fractional differaccumulators; fractional difference equations; fractional differencing; fractional frequency responses; fractional linear systems; fractional poles; hyperbolic process; impulse response; parabolic noise; special linear systems; stochastic process; transfer function; zeros;

fLanguage

English

Journal_Title

Vision, Image and Signal Processing, IEE Proceedings -

Publisher

iet

ISSN

1350-245X

Type

jour

DOI

10.1049/ip-vis:20000273

Filename

842720