Wavelet analysis and synthesis are becoming highly important in the area of signal processing. Therefore, it is felt that undergraduate students should be exposed to the rudiments of this treatment before they graduate. A scheme for an elementary coverage of this topic with required minimum amount of mathematics is discussed in this paper. 1.Introduction One of the major Signal Processing tools...

REFERENCIAS Y ENLACES [1] D. P. Kelly, J. T. Sheridan, W. T. Rhodes, “Finite-aperture effects for Fourier transform systems with convergent illumination: Part I. 2-D System analysis”, Opt. Commun. 263, 171-179 (2006). [2] D. P. Kelly, J. T. Sheridan, W. T. Rhodes, “Finite-aperture effects for Fourier transform systems with convergent illumination: Part II. 3-D System analysis”, Opt. Commun. 263...

Let G = SpecA be a linearly reductive group, and wG ∈ A ∗ be G-invariant and wG(1) = 1. We establish the harmonic analysis on G and we compute wG when G = Sln, Gln, On, Sp2n, by geometric arguments and by means of the Fourier transform. Introduction An affine k-group G = SpecA is semisimple if and only if A splits in the form A = k ×B∗ as k-algebras, where the first projection π1 : A → k is the...

By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the timefrequency characteristics of signals which exhibit transient oscillatory behavior. Since the resulting representations depend on the choice of the window functions, it is important to know how they influence the analyses. One ...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...

This chapter covers the fundamental principles and current applications of Fourier transform (FT) infrared and Fourier transform Raman spectroscopies as utilized in the analysis of polymeric materials. The primary emphasis of the first part is on the principles and advantages of these interferometric methods, whereas the remaining sections illustrate numerous applications focusing on the struct...

Let D be a bounded domain in Rn such that ∂D is a union of a finite number of smooth hypersurfaces in general position. The asymptotics of the Fourier transform of a piece-wise smooth function f(x) with discontinuities of the first kind on ∂D, in particular of the characteristic function of D, is found in almost all directions. The results are based on our recent work on the singularities of th...

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is...

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...