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2015•Unpublished venueRequires access

Fourier Transforms on Finite Abelian Groups

D.R.G. Hulzebos

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Abstract

In this research the Fourier transform on finite abelian groups is studied. To define this transform, characters are introduced. After the Fourier transform has been defined, an algorithm that will improve the computation time needed to do the Fourier transform is recalled. After this two applications of the Fourier transform will be discussed. In these applications the Fourier transform will be used to multiply huge integers in a faster way and to put watermarks on music.

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What this paper is about

In this research the Fourier transform on finite abelian groups is studied. To define this transform, characters are introduced. After the Fourier transform has been defined, an algorithm that will improve the computation time needed to do the Fourier transform is recalled. After this two applications of the Fourier transform will be discussed. In these applications the Fourier transform will be used to multiply huge integers in a faster way and to put watermarks on music.

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Available abstract

In this research the Fourier transform on finite abelian groups is studied. To define this transform, characters are introduced. After the Fourier transform has been defined, an algorithm that will improve the computation time needed to do the Fourier transform is recalled. After this two applications of the Fourier transform will be discussed. In these applications the Fourier transform will be used to multiply huge integers in a faster way and to put watermarks on music.

Key concepts: Fourier transform on finite groups, Fourier transform, Fractional Fourier transform, Discrete Fourier transform (general), Fourier inversion theorem, Hartley transform, Short-time Fourier transform, Non-uniform discrete Fourier transform

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