2009digital Encyclopedia of Applied PhysicsRequires access

F ourier and Other Mathematical Transforms

R. N. Bracewell

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Abstract

Abstract The article contains sections titled: Introduction The Fourier Transform Continuous versus Discrete Transforms Some Common Transforms The Laplace Transform Convergence Conditions Why Transforms are Useful Fields of Application The H artley Transform The Fast Fourier Transform The Fast H artley Algorithm The M ellin Transform The H ilbert Transform Multidimensional Transforms The H ankel Transform The A bel Transform Tomography and the Radon Transform The W alsh Transform The Z Transform Convolution Summary

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What this paper is about

Abstract The article contains sections titled: Introduction The Fourier Transform Continuous versus Discrete Transforms Some Common Transforms The Laplace Transform Convergence Conditions Why Transforms are Useful Fields of Application The H artley Transform The Fast Fourier Transform The Fast H artley Algorithm The M ellin Transform The H ilbert Transform Multidimensional Transforms The H ankel Transform The A bel Transform Tomography and the Radon Transform The W alsh Transform The Z Transform Convolution Summary

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Available abstract

Abstract The article contains sections titled: Introduction The Fourier Transform Continuous versus Discrete Transforms Some Common Transforms The Laplace Transform Convergence Conditions Why Transforms are Useful Fields of Application The H artley Transform The Fast Fourier Transform The Fast H artley Algorithm The M ellin Transform The H ilbert Transform Multidimensional Transforms The H ankel Transform The A bel Transform Tomography and the Radon Transform The W alsh Transform The Z Transform Convolution Summary

Key concepts: Hartley transform, Fractional Fourier transform, Radon transform, Discrete Fourier transform (general), Discrete Hartley transform, Two-sided Laplace transform, S transform, Mellin transform

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