Differentiation by Fourier transformation and its connection with differentiation by finite differencing

Compani-Tabrizi, Behrooz; Geyer, Richard G.

doi:10.1090/qam/860902

Online ISSN 1552-4485; Print ISSN 0033-569X

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Differentiation by Fourier transformation and its connection with differentiation by finite differencing

Authors: Behrooz Compani-Tabrizi and Richard G. Geyer
Journal: Quart. Appl. Math. 44 (1986), 519-528
MSC: Primary 65D25; Secondary 65T05
DOI: https://doi.org/10.1090/qam/860902
Comment: Quart. Appl. Math. 47 (1989), 309-311.
MathSciNet review: 860902
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Abstract: The relation between central-, forward-, and backward-finite differencing and differentiation by Fourier transformation is developed. The conventional rule for differentiation by Fourier transformation of a discretized function, namely, multiplication of the Fourier transform of the function by $ik$ and a subsequent inverse Fourier transformation, is shown to be a first-order approximation to more complete rules. Numerical examples are provided.