Fourier series

About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.

Fourier series for analysis of temporal sequences of satellite sensor imagery

Abstract: Fourier Series and the derivative were used in this study for analysing time series of remotely-sensed data. The technique allows fundamental characteristics of time series data to be quantified. In Fourier analysis a function in space or time is broken down into sinusoidal components, or harmonics. The first and second harmonics are a function of the mono or bi-modality of the curve, demonstrated in the study on Global Vegetation Index data classified into typical mono and bi-modal vegetation index zones. The last harmonic explains close to 100 per cent of the variance in the curve. Other important parameters of the time series, such as extreme points and rate of change, can be extracted from the derivative of the Fourier Series. Fourier Series may form a basis for a quantitative approach to the problem of handling temporal sequences of remotely-sensed data.

A Complete Set of Fourier Descriptors for Two-Dimensional Shapes

Abstract: A set of Fourier descriptors for two-dimensional shapes is defined which is complete in the sense that two objects have the same shape if and only if they have the same set of Fourier descriptors. It also is shown that the moduli of the Fourier coefficients of the parameterizing function of the boundary of an object do not contain enough information to characterize the shape of an object. Further a relationship is established between rotational symmetries of an object and the set of integers for which the corresponding Fourier coefficients of the parameterizing function are nonzero.

Lifting-Line Analysis for Twisted Wings and Washout-Optimized Wings

Abstract: A more practical form of the analytical solution for the effects of geometric and aerodynamic twist (washout) on the low-Mach-number performance of a finite wing of arbitrary planform is presented. This infinite series solution is based on Prandtl's classical lifting-line theory and the Fourier coefficients are presented in a form that only depends on wing geometry

Fourier Theoretic Probabilistic Inference over Permutations

Abstract: Permutations are ubiquitous in many real-world problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are n! possibilities, and typical compact and factorized probability distribution representations, such as graphical models, cannot capture the mutual exclusivity constraints associated with permutations. In this paper, we use the "low-frequency" terms of a Fourier decomposition to represent distributions over permutations compactly. We present Kronecker conditioning, a novel approach for maintaining and updating these distributions directly in the Fourier domain, allowing for polynomial time bandlimited approximations. Low order Fourier-based approximations, however, may lead to functions that do not correspond to valid distributions. To address this problem, we present a quadratic program defined directly in the Fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions. We demonstrate the effectiveness of our approach on a real camera-based multi-person tracking scenario.