Adjoint Analysis of Guidance Systems for Time-Series Inputs Using Fourier Analysis

2020 ◽  
Vol 43 (7) ◽  
pp. 1359-1364
Author(s):  
Joel Alpert
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Guidance Systems ◽  
Adjoint Analysis

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

Fourier Analysis of Time Series

2010 ◽  
pp. 545-545
Author(s):  
Joris C Verster ◽  
Thomas M. Tzschentke ◽  
Kieran O’Malley ◽  
Francis C Colpaert ◽  
Bart Ellenbroek ◽  
...  
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Analysis Of Time Series

Chebyshev Spectra Resistance to Trend of Random Noise

2018 ◽  
Vol 17 (03) ◽  
pp. 1850028 ◽  
Author(s):  
Boris M. Grafov ◽  
Alexey L. Kluev ◽  
Tatyana B. Kabanova ◽  
Alexey D. Davydov
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Fourier Analysis ◽  
Random Process ◽  
Chebyshev Polynomials ◽  
Random Noise ◽  
Spectral Lines ◽  
Spectral Approach ◽  
Experimental Conditions ◽  
Strong Trend

Spectral analysis of random noise in the space of discrete Chebyshev polynomials is an alternative to spectral Fourier analysis. The importance of Chebyshev spectral approach is associated with the fact that the discrete Chebyshev transformation of the [Formula: see text]-th order eliminates automatically the polynomial trend of the ([Formula: see text]−1) order. Using the method of artificial trend, it was found that, under the real experimental conditions, the intensity of Chebyshev spectral lines with numbers higher than 1 is resistant to a strong trend of random process. This effect is observed when we use both the arithmetic averaging and the median. The Chebyshev spectral approach is a powerful tool for spectral analysis of random time series with a strong trend.

scholarly journals Assessing drought cycles in SPI time series using a Fourier analysis

2015 ◽  
Vol 15 (3) ◽  
pp. 571-585 ◽  
Author(s):  
E. E. Moreira ◽  
D. S. Martins ◽  
L. S. Pereira
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
North Atlantic ◽  
Clustering Analysis ◽  
Standardized Precipitation Index ◽  
The North ◽  
Southern Portugal ◽  
Circulation Indices ◽  
The Common ◽  
The North Atlantic Oscillation

Abstract. In this study, drought in Portugal was assessed using 74 time series of Standardized Precipitation Index (SPI) with a 12-month timescale and 66 years length. A clustering analysis on the SPI Principal Components loadings was performed in order to find regions where SPI drought characteristics are similar. A Fourier analysis was then applied to the SPI time series considering one SPI value per year relative to every month. The analysis focused on the December SPI time series grouped in each of the three identified clusters to investigate the existence of cycles that could be related to the return periods of droughts. The most frequent significant cycles in each of the three clusters were identified and analysed for December and the other months. Results for December show that drought periodicities vary among the three clusters, pointing to a 6-year cycle across the country and a 9.4-year cycle in central and southern Portugal. Both these cycles likely show the influence of the North Atlantic Oscillation (NAO) on the occurrence and severity of droughts in Portugal. Relative to other months it was observed that cycles varied according to the common occurrence of precipitation: for the rainy months – November, December and January – cycles are similar to those for December; for the dry months – May to September – where the lack of precipitation masks the occurrence of drought, the dominant cycles are of short duration and cannot be related to the NAO or other large circulation indices to explain drought variability; for the transition months – February, March, April and October – 6-year and 3-year cycles were identified, the latter being more strongly apparent in central and southern Portugal. NAO influence is again identified relative to the 6-year cycles. The short cycles are apparently associated with positive SPI, thus with wetness, not drought. Overall, results confirm the importance of the NAO as a driving force for dry and wet periods.

scholarly journals Advantages Of A Time Series Analysis Using Wavelet Transform As Compared With A Fourier Analysis

2015 ◽  
Vol 23 (2) ◽  
pp. 30-36 ◽  
Author(s):  
Patrik Sleziak ◽  
Kamila Hlavčová ◽  
Ján Szolgay
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Time Series Analysis ◽  
Fourier Analysis ◽  
Stationary Time Series ◽  
Precipitation Time Series ◽  
Software Environment ◽  
R Software ◽  
Series Analysis ◽  
Average Annual Precipitation

Abstract The paper presents an analysis of changes in the structure of the average annual discharges, average annual air temperature, and average annual precipitation time series in Slovakia. Three time series with lengths of observation from 1961 to 2006 were analyzed. An introduction to spectral analysis with Fourier analysis (FA) is given. This method is used to determine significant periods of a time series. Later in this article a description of a wavelet transform (WT) is reviewed. This method is able to work with non-stationary time series and detect when significant periods are presented. Subsequently, models for the detection of potential changes in the structure of the time series analyzed were created with the aim of capturing changes in the cyclical components and the multiannual variability of the time series selected for Slovakia. Finally, some of the comparisons of the time series analyzed are discussed. The aim of the paper is to show the advantages of time series analysis using WT compared with FT. The results were processed in the R software environment.

scholarly journals Extracting oscillation frequencies from data: various approaches

2013 ◽  
Vol 9 (S301) ◽  
pp. 77-84 ◽  
Author(s):  
C. A. Engelbrecht
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Major Part ◽  
Statistical Tools ◽  
The Past ◽  
Alternative Approaches ◽  
Periodic Signals ◽  
Oscillation Frequencies

AbstractAsteroseismology depends absolutely on the detection of authentic pulsation signatures in stars. A variety of mathematical and statistical tools have been developed to extract such signatures from photometric and spectroscopic time series. The earliest tools were developed on the platform of Fourier analysis, and Fourier-based methodology still plays a major part in the detection of pulsation signatures in the present day. Alternative approaches have been gaining ground in recent years. This article offers a brief but broad review of the various methodologies for detecting authentic periodic signals that have been developed over the past few decades, including examples of their pitfalls and successes.

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