Abstract—This work deals with the analysis of the impact of additive noise on the geometrical features of the space vector shape on the complex plane. The space vector shape is of great importance in the power quality analysis of modern three-phase power systems since its geometrical features are closely related to the voltage supply quality. In case of voltage sag or swell the space vector sha...

Natalia A. Schmid, Yoram Bresler, and Pierre Moulin University of Illinois at Urbana-Champaign Coordinated Science Laboratory, 1308 West Main, Urbana, IL 61801 nschmid ifp.uiuc.edu, ybresler uiuc.edu, moulin ifp.uiuc.edu ABSTRACT We consider the estimation of an unknown arbitrary 2D object shape from sparse noisy samples of its Fourier transform. The estimate of the closed boundary curve is par...

In this section we discuss the theory of Fourier Series for functions of a real variable. In the next sections we will study an analogue which is the “discrete” Fourier Transform. Early in the Nineteenth century, Fourier studied sound and oscillatory motion and conceived of the idea of representing periodic functions by their coefficients in an expansion as a sum of sines and cosines rather tha...

7 Periodic Series and Functions 128 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 128 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 130 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 131 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 133 7.5 The Exponential of a Complex Number . . . . . . . . . . . . . 133 7.6...

The Fourier Descriptor (FD) is a powerful tool for shape analysis and many signatures have been proposed to derive Fourier descriptors. These shape signatures lack of important information in articulation and part structures of complex shapes. In this study, the Inner-Centroid Distance (ICDs) signature which is based on the Centroid Distance signature and Inner-Distance is developed to overcome...

This paper touches upon several traditional topics of 1D linear complex analysis including distribution of zeros of entire functions, completeness problem for complex exponentials and for other families of special functions, some problems of spectral theory of selfadjoint differential operators. Their common feature is the close relation to the theory of complex Fourier transform of compactly s...

This paper proposes new image compression technique that uses Real Fourier Transform. Discrete Fourier Transform (DFT) contains complex exponentials. It contains both cosine and sine functions. It gives complex values in the output of Fourier Transform. To avoid these complex values in the output, complex terms in Fourier Transform are eliminated. This can be done by using coefficients of Discr...

-Determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision application. However, the usual normalization methods are inapplicable when the shape is N-fold rotationally-symmetric (N > = 3). In this paper, an efficient and reliable new method using modified Fourier transform is introduced to normalize such a 2D rotationally-symmetri...

The region occupied by and the contour of a physical object in 3-dimensional space are in a way dual or interchangeable characteristics of the object: the contour is the region’s boundary and the region is contained inside the contour. In the same way the characterization of the object’s contour by its Fourier descriptors, and the reconstruction of its region from the object’s multidimensional ...

In the present paper, we give a brief review of L 1-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.