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Gautschi, Walter

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

Numer. Math. 18, 373-400 (1972).
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Cited in 3 Reviews
Cited in 18 Documents

MSC:

65T40 Numerical methods for trigonometric approximation and interpolation
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\textit{W. Gautschi}, Numer. Math. 18, 373--400 (1972; Zbl 0231.65101)
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References:

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[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).
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