Frequency-domain analysis and tuning of the algebraic differentiators

ABSTRACT

The algebraic differentiators introduced by Mboup, Join and Fliessare studied in the frequency domain. The study complements the time-domain developments of the previous reference where a least-squares interpretation has allowed to explain the main properties of the method and also to devise efficient differentiators. The frequency-domain analysis gives answers to the central question of the choice of the algebraic differentiator parameters. Also, an interpretation of the algebraic differentiators in terms of wavelet decomposition is given.

KEYWORDS:

• Algebraic differentiators
• Fourier transform
• Confluent hypergeometric function

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. These polynomials should be noted as P ^{κ + n, μ + n} _i (τ), but we drop the dependence to n to ease the notations.