A Closed-Form IIR Approximation of Fractional Operator s^ Around a Prescribed Low Frequency

• Published in: IEEE signal processing letters 2024, Vol.31, p.1454-1458
• Main Authors: Ali, Talal Ahmed Ali, Xiao, Zhu, Albdairi, Ahmed Jawad, Jiang, Hongbo
• Format: Article
• Language: English
• Subjects: Complexity theory; Continued fraction expansion; Design methodology; Finite wordlength effects; fractional-order operator; IIR filters; modified indirect discretization; Polynomials; Solids; Transfer functions
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2024.3402165

This letter proposes a closed-form design method for an infinite impulse response (IIR) digital approximation of the fractional-order operator s^{\nu }, \nu \in (-1,1), with improved performance around a predefined low frequency \beta, 0 < \beta < 1. The proposed method utilizes a modified indirect discretization strategy, where it generates a rational s-domain expression using the continued fraction expansion (CFE) of a scaled operator (s/\beta)^{\nu } to minimize the truncation error around \beta. The s-domain expression is then discretized using a well-matched s-to-z transformation and scaled back by \beta ^{\nu } to fit s^{\nu }. The new approximations are compared with recently-proposed models by simulation in terms of frequency response as well as QRS complex detection. The proposed method shows a great potential to attain low-order accurate models that can be immediately used for hardware realizations in a wide range of applications.