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
Comment: Quart. Appl. Math. 47 (1989), 309-311.
MathSciNet review: 860902
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 and a subsequent inverse Fourier transformation, is shown to be a first-order approximation to more complete rules. Numerical examples are provided.