Abstract
In this note, we report a simple proof that Bessel polynomials satisfy maximally flat group delay requirement for low-pass filters.
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Notes
Of course, one may finally define the transfer function as \(H(s) = \theta _n(0)/\theta _n(s)\), in order to have \(H(0)=1\).
References
I.M. Filanovsky, One simple method for the derivation of Bessel (Thomson) filter transfer functions. Int. J. Electr. Eng. Edu. 18(2), 90–92 (1981)
I.M. Filanovsky, Enhancing amplifiers/filters bandwidth by transfer function zeros, in Proceedings ISCAS 2015, (Lisbon, Portugal, 2015) pp. 141–144; IEEExplore 07168590.pdf
E. Grosswald, Bessel Polynomials, vol. 698, Lecture Notes in Mathematics (Springer, Berlin, 1978)
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Carimalo, C. Maximally Flat Group Delay of Bessel Polynomials. Circuits Syst Signal Process 37, 5174–5177 (2018). https://doi.org/10.1007/s00034-018-0812-x
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DOI: https://doi.org/10.1007/s00034-018-0812-x