A Closed-Form IIR Approximation of Fractional Operator [Formula Omitted] Around a Prescribed Low Frequency

• Published in: IEEE signal processing letters Vol. 31; p. 1454
• Main Authors: Talal Ahmed Ali Ali, Zhu, Xiao, Albdairi, Ahmed Jawad, Jiang, Hongbo
• Format: Journal Article
• Language: English
• Published: New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.01.2024
• Subjects: Approximation; Closed form solutions; Discretization; Exact solutions; Frequency response; Impulse response; Low frequencies; Operators (mathematics); Truncation errors
• 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 [Formula Omitted], [Formula Omitted], with improved performance around a predefined low frequency [Formula Omitted], [Formula Omitted]. The proposed method utilizes a modified indirect discretization strategy, where it generates a rational [Formula Omitted]-domain expression using the continued fraction expansion (CFE) of a scaled operator [Formula Omitted] to minimize the truncation error around [Formula Omitted]. The [Formula Omitted]-domain expression is then discretized using a well-matched [Formula Omitted]-to-[Formula Omitted] transformation and scaled back by [Formula Omitted] to fit [Formula Omitted]. 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.