Abstract
The application of the fast-Fourier-transform (FFT) algorithm to calculating one-dimensional and bi-dimensional (temporal and spatial), power and cross-power (coherence and phase) spectra is examined for solar photospheric fluctuations. Alternative methods for smoothing raw spectra, direct averaging (employing various weights) and indirect truncation of the correlation function, are compared, and indirect smoothing is compared with spectra calculated by mean-lagged-product (MLP) methods. Besides providing the raw spectrum, FFT techniques easily allow computing a series of spectra with varying amounts of smoothing. From these spectra a range of satisfactory compromise between resolution and stability can be determined which helps in the interpretation of spectral trends, and in identifying more clearly the existence and significance of spectral features. For bi-dimensional spectra presented as contour plots, this range of satisfactory smoothing can be restricted, particularly when spectral trends must be represented by small-scale contours. Equivalent spectra (i.e. comparable equivalent degrees of freedom) computed or smoothed by different methods have minor, but not negligible, differences. Examination of these differences favors computing of FFT spectra smoothed by averaging for photospheric fluctuations.
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References
Bartlett, M. S.: 1950, Biometrica 37, 1.
Benignus, V. A.: 1969, Trans. IEEE AU-17, 145 and AU-18, 320.
Bingham, C., Godfrey, M. D. and Tukey, J. W.: 1967, Trans. IEEE AU-15, 56.
Blackman, R. B. and Tukey, J. W.: 1958, The Measurement of Power Spectra, Dover Publications, New York.
Brault, J. W. and White, O. R.: 1971, Astron. Astrophys. 13, 169.
Cooley, J. W., Lewis, P. A. W., and Welch, P. D.: 1967, J. Sound Vib. 12, 315 and 339.
Edmonds, F. N., Jr.: 1962, Astrophys. J. 136, 507.
Edmonds, F. N., Jr.: 1966, Astrophys. J. 144, 743 (Appendix).
Edmonds, F. N., Jr.: 1972, Solar Phys., in press.
Edmonds, F. N., Jr., Michard, R., and Servajean, R.: 1965, Ann. Astrophys. 28, 534.
Evans, J. W. and Michard, R.: 1962, Astrophys. J. 135, 812.
Gentleman, W. M. and Sande, G.: 1966, Proc. Amer. Fed. Inf. Proc. Socs. 29, 563.
Hannan, E. J.: 1970, Multiple Time Series, John Wiley and Sons, Inc., New York, Chap. V.
Parzen, E.: 1968, Technical Report No. 11, Dept. of Statistics, Stanford University, Stanford, Calif.
Richardson, R. S. and Schwarzschild, M.: 1950, Astrophys. J. 111, 351.
Sloane, E. A.: 1969, Trans. IEEE AU-17, 133.
Tick, L. J.: 1967, in Harris, B. (ed.), Advanced Symposium on Spectral Analysis of Time Series, John Wiley and Sons, Inc., New York, p. 133.
Tukey, J. W.: 1967, in Harris, B. (ed.), Advanced Symposium on Spectral Analysis of Time Series, John Wiley and Sons, Inc., New York, p. 25.
Webb, C. J.: 1970, Applied Research Laboratories Report ARL-TR-70–22, The University of Texas at Austin.
Welch, P. D.: 1967, IEEE Trans. AU-15, 70.
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Edmonds, F.N., Webb, C.J. Spectral analyses of solar photospheric fluctuations. Sol Phys 22, 276–296 (1972). https://doi.org/10.1007/BF00148696
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DOI: https://doi.org/10.1007/BF00148696