scholarly journals A New Algorithm to Accelerate Harmonic Analysis of Time Series

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Pedro A. Martínez-Ortiz ◽  
José M. Ferrándiz
Keyword(s):  
Time Series ◽  
Harmonic Analysis ◽  
Functional Model ◽  
Computation Time ◽  
Spectral Content ◽  
Specific Analysis ◽  
Linear And Nonlinear ◽  
Scalar Time Series ◽  
Secular Terms ◽  
Analysis Of Time Series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.

scholarly journals Optimal Estimate of Global Biome—Specific Parameter Settings to Reconstruct NDVI Time Series with the Harmonic ANalysis of Time Series (HANTS) Method

2021 ◽  
Vol 13 (21) ◽  
pp. 4251
Author(s):  
Jie Zhou ◽  
Li Jia ◽  
Massimo Menenti ◽  
Xuan Liu
Keyword(s):  
Remote Sensing ◽  
Time Series ◽  
Harmonic Analysis ◽  
Remote Sensing Data ◽  
Atmospheric Conditions ◽  
Reconstruction Performance ◽  
Ndvi Time Series ◽  
Harmonic Components ◽  
Analysis Of Time Series ◽  
Optimal Settings

Terrestrial remote sensing data products retrieved from radiometric measurements in the optical and thermal infrared spectrum such as vegetation spectral indices can be heavily contaminated by atmospheric conditions, including cloud and aerosol layers. This contamination results in gaps or noisy observations. The harmonic analysis of time series (HANTS) has been widely used for time series reconstruction of remote sensing imagery in recent decades. To use HANTS model, a series of parameters, such as number of frequencies (NF), fitting error tolerance (FET), degree of over-determinedness (DoD), and regularization factor (Delta), need to be defined by users. These parameters provide flexibilities, but also make it difficult for non-expert users to determine appropriate settings for specific applications. This study systematically evaluated the reconstruction performance of the model under different parameter setting scenarios by simulating pixel-wise reference and noisy NDVI time series. The results of these numerical experiments were further used to identify optimal settings and improve global NDVI reconstruction performance. The results suggested optimal settings for different areas (local optimization). If a user opts to use unique settings for global reconstruction, the setting NF = 4, FET = 0.05, DoD = 5, and Delta = 0.5 can produce the best performance across all setting scenarios (global optimization). In addition, several internal improvements, such as dynamic weighting scheme, polynomial and inter-annual harmonic components, and ancillary attributes of input data can be used to further improve the performance of reconstruction. With these results, future non-expert users can easily determine appropriate settings of HANTS for specific applications in different regions.

Data‐adaptive polarization filters for multichannel geophysical data

Geophysics ◽  
1981 ◽  
Vol 46 (10) ◽  
pp. 1423-1431 ◽  
Author(s):  
J. C. Samson ◽  
J. V. Olson
Keyword(s):  
Time Series ◽  
Seismic Data ◽  
Adaptive Filters ◽  
Spectral Content ◽  
Temporal Features ◽  
Wide Range ◽  
Data Adaptive ◽  
Vector Time Series ◽  
Multichannel Seismic Data ◽  
Scalar Time Series

The design of data‐adaptive filters requires that the noise be defined, statistically or otherwise, by parameters which allow some means of separating the noise from the signal. We consider here multichannel data in which one knows only that the noise is less polarized than the signal in a unitary space. This description of the noise is not sufficient for designing filters which are optimum in any sense; consequently, the filters may require a number of changes in the parameters before a satisfactory design can be found. Once this design has been achieved, the filters can be used to enhance waveforms of arbitrary shape, requiring little prior knowledge of the spectral content or temporal features of the signal. In contrast to many other data‐adaptive filters which give a scalar time‐series output, the filters we describe here with vector time series input have an equal number of input and output channels. A number of examples of filtered magnetic and seismic data are given in order to emphasize the wide range of uses for the filters. Some suggestions for application of the filters to multichannel seismic data are given.

scholarly journals Comparison of Harmonic Analysis of Time Series (HANTS) and Multi-Singular Spectrum Analysis (M-SSA) in Reconstruction of Long-Gap Missing Data in NDVI Time Series

2020 ◽  
Vol 12 (17) ◽  
pp. 2747
Author(s):  
Hamid Reza Ghafarian Malamiri ◽  
Hadi Zare ◽  
Iman Rousta ◽  
Haraldur Olafsson ◽  
Emma Izquierdo Verdiguier ◽  
...  
Keyword(s):  
Time Series ◽  
Missing Data ◽  
Harmonic Analysis ◽  
Spectrum Analysis ◽  
Singular Spectrum Analysis ◽  
Vegetation Changes ◽  
Singular Spectrum ◽  
Ndvi Time Series ◽  
Reconstructed Data ◽  
Analysis Of Time Series

Monitoring vegetation changes over time is very important in dry areas such as Iran, given its pronounced drought-prone agricultural system. Vegetation indices derived from remotely sensed satellite imageries are successfully used to monitor vegetation changes at various scales. Atmospheric dust as well as airborne particles, particularly gases and clouds, significantly affect the reflection of energy from the surface, especially in visible, short and infrared wavelengths. This results in imageries with missing data (gaps) and outliers while vegetation change analysis requires integrated and complete time series data. This study investigated the performance of HANTS (Harmonic ANalysis of Time Series) algorithm and (M)-SSA ((Multi-channel) Singular Spectrum Analysis) algorithm in reconstruction of wide-gap of missing data. The time series of Normalized Difference Vegetation Index (NDVI) retrieved from Landsat TM in combination with 250m MODIS NDVI time image products are used to simulate and find periodic components of the NDVI time series from 1986 to 2000 and from 2000 to 2015, respectively. This paper presents the evaluation of the performance of gap filling capability of HANTS and M-SSA by filling artificially created gaps in data using Landsat and MODIS data. The results showed that the RMSEs (Root Mean Square Errors) between the original and reconstructed data in HANTS and M-SSA algorithms were 0.027 and 0.023 NDVI value, respectively. Further, RMSEs among 15 NDVI images extracted from the time series artificially and reconstructed by HANTS and M-SSA algorithms were 0.030 and 0.025 NDVI value, respectively. RMSEs of the original and reconstructed data in HANTS and M-SSA algorithms were 0.10 and 0.04 for time series 6, respectively. The findings of this study present a favorable option for solving the missing data challenge in NDVI time series.

Crop identification using harmonic analysis of time-series AVHRR NDVI data

2002 ◽  
Vol 37 (1-3) ◽  
pp. 127-139 ◽  
Author(s):  
Mark E Jakubauskas ◽  
David R Legates ◽  
Jude H Kastens
Keyword(s):  
Time Series ◽  
Harmonic Analysis ◽  
Analysis Of Time Series
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