Search results for "Orthogonal functions"
showing 8 items of 8 documents
Multiple-Output Walsh Function Generation for Minimum Orthogonality Error
1978
A hazard-free multiple-output Walsh function generator is presented which requires a minimum amount of hardware and is as fast as the integrated logic family employed for the implementation. However, the main characteristic of the instrument is the optimum performance from the viewpoint of the orthogonality of the function generated, as it is shown by the experimental verifications reported.
Lévy flights in an infinite potential well as a hypersingular Fredholm problem.
2016
We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schr\"odinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numer…
Nonlinear PCA for Spatio-Temporal Analysis of Earth Observation Data
2020
Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we pro…
Spatial and temporal temperature trends on the Yunnan Plateau (Southwest China) during 1961-2004
2010
Monthly mean (TEM), maximum (Tmax) and minimum (Tmin) surface air temperatures at 119 meteorological stations on the Yunnan Plateau (YP, Southwest China) were analysed for temporal trends and spatial variation patterns during the period 1961–2004. Linear trend analyses revealed that annual temperature over the YP increased at a rate of 0.3 °C/decade during the period 1961–2004, while warming trend of 0.33 °C/decade and 0.26 °C/decade was observed for winter and summer temperatures, respectively. Warming trends of nighttime minimum temperature are more pronounced than those of daytime maximum temperature, especially during winter season. Consequently, a decreasing trend of diurnal temperatur…
Comparison of measured brightness temperatures from SMOS with modelled ones from ORCHIDEE and H-TESSEL over the Iberian Peninsula
2017
19 pges, 10 figures, 6 tables
Intercomparison and analyses of the climatology of the West African Monsoon in the West African Monsoon Modeling and Evaluation project (WAMME) first…
2010
International audience; This paper briefly presents the West African Monsoon (WAM) Modeling and Evaluation Project (WAMME) and evaluates WAMME general circulation models' (GCM) performances in simulating variability of WAM precipitation, surface temperature, and major circulation features at seasonal and intraseasonal scales in the first WAMME experiment. The analyses indicate that models with specified sea surface temperature generally have reasonable simulations of the pattern of spatial distribution of WAM seasonal mean precipitation and surface temperature as well as the averaged zonal wind in latitude-height cross-section and low level circulation. But there are large differences among mo…
Empirical Orthogonal Function and Functional Data Analysis Procedures to Impute Long Gaps in Environmental Data
2016
Air pollution data sets are usually spatio-temporal multivariate data related to time series of different pollutants recorded by a monitoring network. To improve the estimate of functional data when missing values, and mainly long gaps, are present in the original data set, some procedures are here proposed considering jointly Functional Data Analysis and Empirical Orthogonal Function approaches. In order to compare and validate the proposed procedures, a simulation plan is carried out and some performance indicators are computed. The obtained results show that one of the proposed procedures works better than the others, providing a better reconstruction especially in presence of long gaps.
Orthogonal functions analysis of singular systems with impulsive responses
1990
Presents a systematic study using piecewise-constant orthogonal functions for the analysis of impulsive responses of singular systems. Walsh and block-pulse functions solutions are examined.