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2003•Unpublished venueRequires access

The unified discrete Fourier-Hartley transforms: theory and structure

S. Oraintara

Open publisher page 7 citations

Abstract

In this paper, the theory of the unified discrete Fourier-Hartley transform (UDFHT) is developed. The UDFHT includes the discrete Fourier and Hartley transforms of types I-IV as special cases, and with little modification, it also includes the discrete cosine and sine transforms of types II-IV. A unified efficient structure using fast Fourier transform is proposed. The UDFHT is then generalized (GDFHT) to the case of non-constant coefficients. Sufficient conditions for orthogonality of the transform are presented. The GDFHT can be used to compute the modified discrete cosine transform for both non-window and window modes as illustrated in the paper.

About this research paper

What this paper is about

In this paper, the theory of the unified discrete Fourier-Hartley transform (UDFHT) is developed. The UDFHT includes the discrete Fourier and Hartley transforms of types I-IV as special cases, and with little modification, it also includes the discrete cosine and sine transforms of types II-IV. A unified efficient structure using fast Fourier transform is proposed. The UDFHT is then generalized (GDFHT) to the case of non-constant coefficients. Sufficient conditions for orthogonality of the transform are presented. The GDFHT can be used to compute the modified discrete cosine transform for both non-window and window modes as illustrated in the paper.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the theory of the unified discrete Fourier-Hartley transform (UDFHT) is developed. The UDFHT includes the discrete Fourier and Hartley transforms of types I-IV as special cases, and with little modification, it also includes the discrete cosine and sine transforms of types II-IV. A unified efficient structure using fast Fourier transform is proposed. The UDFHT is then generalized (GDFHT) to the case of non-constant coefficients. Sufficient conditions for orthogonality of the transform are presented. The GDFHT can be used to compute the modified discrete cosine transform for both non-window and window modes as illustrated in the paper.

Key concepts: Discrete Hartley transform, Discrete sine transform, Discrete Fourier transform (general), Hartley transform, Sine and cosine transforms, Discrete cosine transform, Non-uniform discrete Fourier transform, Fractional Fourier transform

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