Fractional Signal Processing

Dear Colleagues,

People involved in the activities of signal processing (SP) know that it has recovered, reinterpreted, reformulated and given meaning to many mathematical theories and tools, and, in parallel, introduced new ones. However, SP has been almost absent in the fractional calculus (FC) world and the reverse is also true, although we know that fractional behavior is present in many of SP’s traditional areas. This is astonishing given that FC has been adopted in recent years to model many natural and human-made phenomena since traditional tools are unable to provide accurate descriptions of their behavior. This is the case, for example, in physics, viscoelasticity, biomedical engineering, electrochemistry, and electromagnetics. Well-known applications include the long-range processes, 1/f noise, fractional chaos, fractional Gaussian noise, and fractional Brownian motion (fBm)

In the last 15 years, many applications have been described and important topics such as analysis, modeling, and synthesis considered. However, a closer look reveals that there are many traditional tools that need to be extended to the fractional frame while maintaining strict compatibility with previous versions. Not all proposed formulations for fractional operators are suitable to accomplish this task: most of them are incompatible with SP theory and practice (for example, RL and C). In fact, we cannot use derivatives in that the derivative of a sinusoid is not a sinusoid, as this prevents us from defining the frequency response of linear systems. Similarly, we must ensure that the derivative of the Heaviside unit step is not null since this impedes us from defining the correct derivative of the impulse. The main objective of this Special Issue is to bring people already involved in SP activities to the FC world.

Topics include, but are not limited to, the following:

• Continuous and discrete shift-invariant systems, namely those based on Liouville-type derivatives;
• Study of fractional scale-invariant systems based on the Hadamard derivatives;
• Time-frequency and time-space systems;
• Fast algorithms for fractional SP;
• Fractional systems modeling and identification;
• Filter design;
• Biomedical signal processing: ECG, EEG, Epilepsy, Sleep classification, Spindles, etc.;
• Fractional electrical circuits;
• New fractional devices for signal processing.

Dr. Manuel Duarte Ortigueira
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Signals is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.