The Fractional Orthogonal Difference with Applications

Mathematics

Enno Diekema¹ 

[1]Kooikersdreef 620, 7328 BS Apeldoorn, The Netherlands

[2] E-Mail

关键词: orthogonal difference;    orthogonal polynomials;    hypergeometric functions;    Fourier transform;    frequency response;   

DOI  :  10.3390/math3020487

来源: mdpi

【 摘 要 】

This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland