Application of fractional-order calculus approach to signal processing

2011 ◽  
Author(s):  
Zheng Wang ◽  
Xianmin Ma
Keyword(s):  
Signal Processing ◽  
Fractional Order ◽  
Fractional Order Calculus

SOME APPLICATIONS OF FRACTIONAL ORDER CALCULUS TO DESIGN DIGITAL FILTERS FOR BIOMEDICAL SIGNAL PROCESSING

2012 ◽  
Vol 12 (02) ◽  
pp. 1240008 ◽  
Author(s):  
YOUCEF FERDI
Keyword(s):  
Signal Processing ◽  
Fractional Order ◽  
Digital Filters ◽  
Sampling Period ◽  
Biomedical Signal Processing ◽  
Mathematical Tool ◽  
Impulse Responses ◽  
Biomedical Signal ◽  
Fractional Order Calculus ◽  
Smoothing Filter

The goal of this paper is to describe some applications of fractional order calculus to biomedical signal processing with emphasis on the ability of this mathematical tool to remove noise, enhance useful information, and generate fractal signals. Three types of digital filters are considered, namely, lowpass differentiation filter, smoothing filter, and 1/fβ-noise generation filter. The filter impulse responses are functions of the fractional order and the sampling period only, and thus can be computed easily. Application examples are presented for illustrations.

Predicting the aggressiveness of peripheral zone prostate cancer using a fractional order calculus diffusion model

2021 ◽  
Vol 143 ◽  
pp. 109913
Author(s):  
Zhihua Li ◽  
Guangyu Dan ◽  
Vikram Tammana ◽  
Scott Johnson ◽  
Zheng Zhong ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Diffusion Model ◽  
Fractional Order ◽  
Peripheral Zone ◽  
Fractional Order Calculus

scholarly journals Studies of anomalous diffusion in the human brain using fractional order calculus

2010 ◽  
Vol 63 (3) ◽  
pp. 562-569 ◽  
Author(s):  
Xiaohong Joe Zhou ◽  
Qing Gao ◽  
Osama Abdullah ◽  
Richard L. Magin
Keyword(s):  
Human Brain ◽  
Fractional Order ◽  
Anomalous Diffusion ◽  
Fractional Order Calculus

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

Formulation of Fractional Derivative-Based De-Hazing Algorithm and Implementation on Mobile-Embedded Devices

2019 ◽  
Vol 19 (01) ◽  
pp. 1950003
Author(s):  
Uche A. Nnolim
Keyword(s):  
Image Processing ◽  
Fractional Derivative ◽  
Mobile Devices ◽  
Fractional Order ◽  
Spatial Filter ◽  
Embedded Devices ◽  
Processing Application ◽  
Fractional Order Calculus ◽  
Image Processing Application ◽  
Logarithmic Image Processing

This paper presents the modification of a previously developed algorithm using fractional order calculus and its implementation on mobile-embedded devices such as smartphones. The system performs enhancement on three categories of images such as those exhibiting uneven illumination, faded features/colors and hazy appearance. The key contributions include the simplified scheme for illumination correction, contrast enhancement and de-hazing using fractional derivative-based spatial filter kernels. These are achieved without resorting to logarithmic image processing, histogram-based statistics and complex de-hazing techniques employed by conventional algorithms. The simplified structure enables ease of implementation of the algorithm on mobile devices as an image processing application. Results indicate that the fractional order version of the algorithm yields good results relative to the integer order version and other algorithms from the literature.

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