A Course in Fourier's Analysis and Periodogram Analysis for the Mathematical Laboratory

I would like to give a description of the high-speed electronic digital calculating machine now in an advanced stage of construction in the University Mathematical Laboratory, Cambridge, and known as the EDSAC (Electronic Delay Storage Automatic Calculator). Before doing this I will set forth some of the considerations underlying its design. It will be realized that the potential power of electronic digital computing machines is very great, and that they are likely to have a far-reaching effect on certain fields of scientific research. It is, for example, often possible to write down the mathematical equations governing a situation but not possible to treat them analytically. If any progress is to be made in these cases it must be by a direct numerical attack on the fundamental equations. There have in recent years been a number of examples of this method. I might mention Professor Hartree’s work on self-consistent fields and Professor Southwell’s relaxation methods. In both cases the equations expressing the physical laws appropriate to the problem are written down and an approximate numerical solution sought without any intervening analysis of the conventional type. This kind of method is in principle of wide application and power, and the reason why it has not been more generally applied is that the labour of carrying out the necessary numerical processes is too great

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Searching for planetary signals in Doppler time series: a performance evaluation of tools for periodogram analysis

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stx664 ◽

2017 ◽

Vol 468 (4) ◽

pp. 3775-3784 ◽

Cited By ~ 6

Author(s):

Matteo Pinamonti ◽

Alessandro Sozzetti ◽

Aldo S. Bonomo ◽

Mario Damasso

Keyword(s):

Time Series ◽

Performance Evaluation ◽

Periodogram Analysis ◽

A Performance

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The accretion process in the magnetic Herbig Ae star HD 104237

Proceedings of the International Astronomical Union ◽

10.1017/s1743921319003880 ◽

2018 ◽

Vol 14 (A30) ◽

pp. 137-137

Author(s):

Markus Schöller ◽

Mikhail A. Pogodin

Keyword(s):

Rotation Period ◽

Primary Component ◽

Stellar Rotation ◽

Spectroscopic Parameters ◽

Disk Wind ◽

Accretion Process ◽

Emission Line Spectrum ◽

Spectroscopic Signatures ◽

Periodogram Analysis ◽

Magnetospheric Accretion

AbstractAfter successfully retrieving the known rotation period P = 42.076 d in the Herbig Ae star HD 101412 using spectroscopic signatures of accretion tracers (Schöller et al.2016), we have studied magnetospheric accretion in the Herbig Ae SB2 system HD 104237 using spectroscopic parameters of the He i 10830, Paγ, and He i 5876 lines, formed in the accretion region. Employing 21 spectra obtained with ISAAC and X-shooter, we found that the temporal behavior of these parameters can be explained by a variable amount of matter being accreted in the region between the star and the observer. Using a periodogram analysis, we examined the possible origin of the accretion flow in HD 104237 and considered the following four scenarios: matter flows from the circumbinary envelope, mass exchange between the system’s components, magnetospheric accretion (MA) from the disk onto the star, and fast high-latitude accretion from a disk wind onto a weakly magnetized star. Based on a correlation analysis, we were able to show that the primary component is responsible for the observed emission line spectrum of the system. Since we do not find any correlation of the spectroscopic parameters with the phase of the orbital period (P ≍ 20 d), we can reject the first two scenarios. We found a variation period of about 5 d, which likely represents the stellar rotation period of the primary and favors the MA scenario.

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Periodogram Analysis and Continuous Spectra

Biometrika ◽

10.2307/2332141 ◽

1950 ◽

Vol 37 (1/2) ◽

pp. 1 ◽

Cited By ~ 27

Author(s):

M. S. Bartlett

Keyword(s):

Periodogram Analysis

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Latitude Dependent Circadian Rhythms of Carabid Beetles

Zeitschrift für Naturforschung C ◽

10.1515/znc-1986-9-1021 ◽

1986 ◽

Vol 41 (9-10) ◽

pp. 935-945

Author(s):

Gisela Leyk ◽

Wolfgang Martin

Keyword(s):

Time Course ◽

Activity Patterns ◽

Carabid Beetles ◽

Constant Darkness ◽

Spectrum Estimation ◽

Program System ◽

Central European ◽

Light Pulses ◽

Different Types ◽

Periodogram Analysis

Abstract Comparative studies of circadian activity rhythms were performed with three stocks of the species Pterostichus rhaeticus Heer (from Southern Europe, Central Europe, and the Subarctic) and with one Central European stock of the sibling species Pterostichus nigrita Paykull. The hehaviour was investigated in various LD conditions, constant conditions including LL with changes of the illumination intensity and constant darkness with light pulses. The data were analysed with the program system “Timesdia” containing various techniques like power spectrum estimation, periodogram analysis and complex demodulation. This allowed to reveal the time course of rhythms and to determine the number of phase jumps as a measure for precision. With the help of these methods, the activity patterns are classified in different types of behaviour: synchronization, temporarily synchronization, aperiodic behaviour, free run, temporarily free run, relative entrainment, and relative coordination. Besides graduated differences between the populations in south-to-north direction (e.g. in the tendency to rhythmic behaviour) the analysis revealed splitting of rhythms into two or even three components of different frequencies and transitions from rhythmic to aperiodic behaviour or vice versa after arbitrarily chosen light pulses in constant darkness. This behaviour cannot be explained by a system which is composed of one single limit cycle oscillator, but the results rather support a multi-oscillator model.

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