Attenuation factors in practical Fourier analysis. (English) Zbl 0231.65101


65T40 Numerical methods for trigonometric approximation and interpolation
Full Text: DOI EuDML


[1] Ahlberg, J. H., Nilson, E. N., Walsh, J. L.: The theory of splines and their application. New York-London: Academic Press 1967. · Zbl 0158.15901
[2] Bauer, F. L., Stetter, H. J.: Zur numerischen Fourier-Transformation. Numer. Math.1, 208-220 (1959). · Zbl 0096.10401
[3] Chao, F. H.: A new method of practical harmonic analysis [Chinese]. Acta Math. Sinica6, 433-451 (1956). · Zbl 0075.28801
[4] Cooley, J. W., Tukey, J. W.: An algorithm for the machine calculation of complex Fourier series. Math. Comp.19, 297-301 (1965). · Zbl 0127.09002
[5] ?, Lewis, P. A. W., Welch, P. D.: The fast Fourier transform and its applications. IEEE Trans. Education E-12, 27-34 (1969).
[6] Dällenbach, W.: Verschärftes rechnerisches Verfahren der harmonischen Analyse. Arch. Elektrotechnik10, 277-282 (1921).
[7] Eagle, A.: On the relations between the Fourier constants of a periodic function and the coefficients determined by harmonic analysis. Philos. Mag.5 (7), 113-132 (1928). · JFM 54.0580.05
[8] Ehlich, H.: Untersuchungen zur numerischen Fourieranalyse. Math. Z.91, 380-420 (1966). · Zbl 0143.38902
[9] Gentleman, W. M., Sande, G.: Fast Fourier transforms-for fun and profit, 1966 Fall Joint Computer Conference, AFIPS Proc., vol. 29. Washington D. C.: Spartan 1966.
[10] Golomb, M.: Approximation by periodic spline interpolants on uniform meshes. J. Approximation Theory1, 26-65 (1968). · Zbl 0185.30901
[11] Hildebrand, F. B.: Introduction to numerical analysis. New York: McGraw-Hill 1956. · Zbl 0070.12401
[12] Oumoff, N.: Sur l’application de la méthode de Mr. Ludimar Hermann à l’analyse des courbes périodiques. Le Physiologiste Russe1, 52-64 (1898/99).
[13] Quade, W., Collatz, L.: Zur Interpolationstheorie der reellen periodischen Funktionen. Sitzungsber. Preuss. Akad. Wiss.30, 383-429 (1938). · JFM 65.0543.01
[14] Runge, C.: Theorie und Praxis der Reihen. Leipzig: G. J. Göschen’sche Verlagshandlung 1904. · JFM 35.0246.01
[15] Salzer, H. E.: Formulas for calculating Fourier coefficients. J. Math. Phys.36, 96-98 (1957). · Zbl 0080.11403
[16] Schoenberg, I. J.: On spline interpolation at all integer points of the real axis. Colloquium on the Theory of Approximation of Functions (Cluj, 1967). Mathematica (Cluj)10 (33), 151-170 (1968). · Zbl 0183.33101
[17] Schweikert, D. G.: An interpolation curve using a spline in tension. J. Math. and Phys.45, 312-317 (1966). · Zbl 0146.14102
[18] Serebrennikov, M. G.: A more exact method of harmonic analysis of empirical periodic curves [Russian]. Akad. Nauk SSSR. Prikl. Mat. Meh.12, 227-232 (1948).
[19] Yu?kov, P. P.: The practical harmonic analysis of empirical functions when the given curve is replaced by another approximating the given one by tracing [Russian]. Akad. Nauk SSSR. In?. Sbornik6, 197-210 (1950).
[20] ?: On the correction of the coefficients obtained in the usual practical harmonic analysis [Russian]. Akad. Nauk SSSR. In?. Sbornik10, 213-222 (1951).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.