PDF Generalized Functions, Vol. 4: Applications of Harmonic Analysis

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Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III.

Israel Gelfand

For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter. Products of distributions wave front sets and oscillatory. Applications to Statistical Mechanics. Appendix Motion on a halfline limit pointlimit circle methods.

Perturbations of selfadjoint operators. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Sanjay Kumar.

Generalized Harmonic Analysis and Tauberian Theorems, Volume 2

The different parameters Received in revised form for the window functions are also obtained with the help of simulations. The fractional 23 March Fourier transformation contains an adjustable parameter with which the main lobe Accepted 13 April width and correspondingly, the minimum stop band attenuation of the resulting Available online 6 May window function can be controlled. All rights reserved.

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Fractional Fourier transform Dirichlet window Hamming window Hanning window 1. Introduction the side lobe leakage, it causes the main lobe to broaden thus, reducing the resolution. This is a trade-off that has to Window functions are used in harmonic analysis to be made, one should choose the window function, which reduce the undesirable effects related to the spectral best suits the application.

Applications of FrFT have also been described Window functions have been successfully used in by Bailey and Swartztrauber et al. Stankovic et al. Also, Sharma et al.

Generalized Functions - Vol 4: Applications of Harmonic Analysis

A complete review of many window functions analysis in fractional Fourier domain to show the and their properties was presented by Harris [2]. In this routines.

An attempt has also been E-mail addresses: sanjay. Kumar , made to study the variations of the parameters Half Main ksingh thapar. Singh , rajiv. Kumar et al. It is found that with the adjustment of parameter a to different values, these window functions can attain a maximum main lobe width and SLFOR. The rest of the paper is organized as follows.

Section 2 gives an overview of the fractional Fourier transform.

Generalized Functions - Izrail Moiseevich Gelfand - Google книги

An overview of the window functions and its parameters are discussed in Section 3. Experimental results are presented in Section 6. The conclusive remarks are presented in Section 7. Log magnitude plot of Dirichlet window to illustrate the 2. The Fourier transform FT is undoubtedly one of the 3.

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Window function and its parameters most valuable and frequently used tools in signal proces- sing and analysis [7—9]. Little need be said of the Window functions are widely used in digital signal importance and ubiquity of the ordinary FT in many areas processing for the applications in signal analysis and of science and engineering.

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The the areas of optics and signal processing [10—13]. Affiliation s HTML :. Abstract: The first systematic theory of generalized functions also known as distributions was created in the early s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. Volume: Publication Month and Year: Copyright Year: Page Count: Cover Type: Hardcover.

Print ISBN Online ISBN Online ISSN:. Primary MSC: Applied Math? MAA Book?

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