Vol. 3, issue 11, article # 14

Kavkyanov S.I., Strepetova S.V. Numerical differentiation of experimental data using the fourier transform. // Atmospheric and oceanic optics. 1990. V. 3. No. 11. P. 1102-1106.
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The conditions under which the Fourier transform can be used for numerical differentiation of functions that are measured with some error are examined. Methods are given for taking into account boundary conditions on the differentiable function and its derivatives. The effect of the uncertainty of the boundary conditions on the quality of the differentiation is studied in a numerical experiment.


1. A.N. Tikhonov and V.Ya. Arsenin, Methods for Solving Improperly Posed Problems (Nauka, Moscow 1986).
2. A.F. Verlan’ and V.S. Sizikov, Integral Equations: Methods, Algorithms, and Programs (Naukova Dumka, Kiev, 1986).
3. G.I. Vasilenko, Theory of Signal Restoration (Sov. Radio, Moscow, 1979).
4. Yu.E. Voskoboinikov and Ya.Ya. Tomsons, Avtometriya, No. 4 (1975).
5. I.D. Gratchev and M.Ch. Salakhov, Avtometriya, No. 2, 35–41 (1985).
6. I.S. Gonorovskjii, Radioelectronic Circuits and Signals (Sov. Radio, Moscow, 1971).
7. R. Otnes and L. Enockson, Applied Time Series Analysis (John Wiley and Sons, New York, 1978).
8. V.E. Zuev and I.E. Naats, Inverse Problems in Laser Sounding of the Atmosphere (Nauka, Moscow, 1982).