Combined and comparative analysis of power spectra

被引:26
作者
Sturrock, PA [1 ]
Scargle, JD
Walther, G
Wheatland, MS
机构
[1] Stanford Univ, Ctr Space Sci & Astrophys, Stanford, CA 94305 USA
[2] NASA, Ames Res Ctr, Moffett Field, CA 94035 USA
[3] Stanford Univ, Dept Stat, Stanford, CA 94305 USA
[4] Univ Sydney, Sch Phys, Sydney, NSW 2006, Australia
基金
美国国家科学基金会;
关键词
D O I
10.1007/s11207-005-7424-x
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been, or one may wish to estimate the significance of a particular peak that shows up in two or more power spectra. One may also on occasion need to search for a complex of peaks in a single power spectrum, such as a fundamental and one or more harmonics, or a fundamental plus sidebands, etc. Visual inspection can be revealing, but it can also be misleading. This leads one to look for one or more ways of forming statistics, which readily lend themselves to significance estimation, from two or more power spectra. We derive formulas for statistics formed from the sum, the minimum, and the product of two or more power spectra. A distinguishing feature of our formulae is that, if each power spectrum has an exponential distribution, each statistic also has an exponential distribution. The statistic formed from the minimum power of two or more power spectra is well known and has an exponential distribution. The sum of two or more powers also has a well-known distribution that is not exponential, but a simple operation does lead to an exponential distribution. Concerning the product of two or more power spectra, we find an analytical expression for the case n = 2, and a procedure for computing the statistic for n > 2. We also show that some quite simple expressions give surprisingly good approximations.
引用
收藏
页码:137 / 153
页数:17
相关论文
共 38 条
  • [1] IS SOLAR NEUTRINO CAPTURE RATE CORRELATED WITH SUNSPOT NUMBER
    BAHCALL, JN
    FIELD, GB
    PRESS, WH
    [J]. ASTROPHYSICAL JOURNAL, 1987, 320 (01) : L69 - L73
  • [2] SOLAR-CYCLE MODULATION OF EVENT RATES IN THE CHLORINE SOLAR NEUTRINO EXPERIMENT
    BAHCALL, JN
    PRESS, WH
    [J]. ASTROPHYSICAL JOURNAL, 1991, 370 (02) : 730 - 742
  • [3] A 154 DAY PERIODICITY IN THE OCCURRENCE RATE OF PROTON FLARES
    BAI, T
    CLIVER, EW
    [J]. ASTROPHYSICAL JOURNAL, 1990, 363 (01) : 299 - 309
  • [4] METHODS OF PERIODICITY ANALYSIS - RELATIONSHIP BETWEEN THE RAYLEIGH ANALYSIS AND A MAXIMUM-LIKELIHOOD METHOD
    BAI, T
    [J]. ASTROPHYSICAL JOURNAL, 1992, 397 (02) : 584 - 590
  • [5] Periodicities in solar flare occurrence: Analysis of cycles 19-23
    Bai, T
    [J]. ASTROPHYSICAL JOURNAL, 2003, 591 (01) : 406 - 415
  • [6] BARTOSZYNKI R, 1996, PROBABILITY STAT INF
  • [7] Bickel P. J., 1977, MATH STAT BASIC IDEA
  • [8] VARIATION OF THE SOLAR NEUTRINO FLUX WITH THE SUNS ACTIVITY
    BIEBER, JW
    SECKEL, D
    STANEV
    STEIGMAN, G
    [J]. NATURE, 1990, 348 (6300) : 407 - 411
  • [9] UPDATE ON THE MEASUREMENT OF THE SOLAR-NEUTRINO FLUX WITH THE HOMESTAKE CHLORINE DETECTOR
    CLEVELAND, BT
    DAILY, T
    DAVIS, R
    DISTEL, J
    LANDE, K
    LEE, CK
    WILDENHAIN, P
    ULLMAN, J
    [J]. NUCLEAR PHYSICS B, 1995, : 47 - 53
  • [10] Measurement of the solar electron neutrino flux with the Homestake chlorine detector
    Cleveland, BT
    Daily, T
    Davis, R
    Distel, JR
    Lande, K
    Lee, CK
    Wildenhain, PS
    Ullman, J
    [J]. ASTROPHYSICAL JOURNAL, 1998, 496 (01) : 505 - 526