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

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 u...

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Bibliographic Details
Published in:IEEE signal processing letters 2024-01, Vol.31, p.1454
Main Authors: Talal Ahmed Ali Ali, Zhu, Xiao, Albdairi, Ahmed Jawad, Jiang, Hongbo
Format: Article
Language:English
Subjects:
Approximation
Closed form solutions
Discretization
Exact solutions
Frequency response
Impulse response
Low frequencies
Operators (mathematics)
Truncation errors
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Summary: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2024.3402165