The intent of this paper is to apply the discrete Fourier transform to the computation of eigenstress and eigenstrain fields around heterogeneities in composite materials. To this end the discrete Fourier transform is first briefly reviewed and then used to solve the basic equations of linear elasticity as pertinent to eigenstrained bodies under external loads. The results of this procedure are...

An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two. The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions. The properties of their autocorrelation functions are studied. The non-periodic complementary sequences are the intersection between anti-symmetric and symme...

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the mul...

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the mul...

The two dimensional fast Fourier transform (2-D FFT) is an indispensable operation in many digital signal processing applications but yet is deemed computationally expensive when performed on a conventional general purpose processors. This paper presents the implementation and performance figures for the Fourier transform on a FPGA-based custom computer. The computation of a 2-D FFT requires O(...

In multi-dimensional signal processing the Cliiord Fourier transform (CFT or in the 2-D case: quater-nionic Fourier transform/QFT) is a consequent extension of the complex valued Fourier transform. Hence, we need a fast algorithm in order to compute the transform in practical applications. Since the CFT is based on a corresponding Cliiord algebra (CA) and CAs are not commutative in general, we ...

A grid method for measuring the shape and strain distribution of 3D objects by using the Fourier transform grid method is presented. In the conventional automated grid method, the position of a line is expressed in an integer, so it is difficult to analyze the accurate position. Using this twodimensional Fourier transform grid method the fault can be overcome by analyzing and interpolating the ...

In this paper we present a new technique for recognising Arabic cursive words from scanned images of text. The approach is segmentation-free, and is applied to four different Arabic typefaces, where ligatures and overlaps pose challenges to segmentation-based methods. We transform each word into a normalised polar image, then we apply a two dimensional Fourier transform to the polar image. The ...

A design of a miniaturized stationary Fourier transform IR spectrometer has been developed that produces a two-dimensional interferogram. The latter is disturbed by effects like parasitic interferences or disparities in the cutoff wavelength of the pixels. Thus, a simple Fourier transform cannot be used to estimate the spectrum of the scene. However, as these defects are deterministic, they can...