Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions

Lima, Paulo Rogério de; Lima, Juliano B.; Souza, Ricardo M. Campello de

doi:10.1007/s00034-016-0447-8

Cited by 7 publications

(2 citation statements)

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“…Note that the symmetries observed in the real and imaginary parts of X are in accordance with what is established in Proposition 3. The analytic signal related to x is obtained from (13), according to what is established in Definition 5; we first construct…”

Section: Examplementioning

confidence: 99%

“…An NTT is usually defined as a Fourier-type transform, where the complex N -th root of unity used as transform kernel is replaced by an N -th root of unity in a finite algebraic structure [1]. Trigonometric number transforms can also be defined; they employ a finite field trigonometry and include cosine, sine and Hartley number transforms, which have analysis and synthesis expressions similar to those of the corresponding real-valued transforms [8,10,13]. Naturally, all computations necessary to calculate an NTT are carried out by using modular arithmetic.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Approach for Defining a Hilbert Number Transform

Lima

Gondim

Souza

2021

Circuits Syst Signal Process

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In this brief, we introduce a new definition for the Hilbert number transform (HNT). Our approach employs concepts related to trigonometry over finite fields and uses as a starting point a specific definition for the Fourier number transform (FNT); one demonstrates that such an FNT allows to define an HNT which is analogous to the real-valued version of the corresponding transform. Additionally, we present a method to obtain the proposed HNT from the recently proposed steerable Fourier number transform.

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Section: Examplementioning

confidence: 99%