Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions
| Autor: | Paulo Lima, Ricardo M. Campello de Souza, Juliano B. Lima |
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| Rok vydání: | 2016 |
| Předmět: |
DFT matrix
Applied Mathematics Mathematical analysis 020206 networking & telecommunications 02 engineering and technology Discrete Hartley transform symbols.namesake Matrix (mathematics) Fourier transform Matrix function Signal Processing Hartley transform 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 020201 artificial intelligence & image processing Eigenvalues and eigenvectors Mathematics Sine and cosine transforms |
| Zdroj: | Circuits, Systems, and Signal Processing. 36:2893-2916 |
| ISSN: | 1531-5878 0278-081X |
| DOI: | 10.1007/s00034-016-0447-8 |
| Popis: | In this paper, we introduce fractional number-theoretic transforms (FrNTT) based on matrix functions. In contrast to previously proposed FrNTT, our approach does not require the construction of any number-theoretic transform (NTT) eigenvectors set. This allows us to obtain an FrNTT matrix by means of a closed-form expression corresponding to a linear combination of integer powers of the respective NTT matrix. Fractional Fourier, Hartley, cosine and sine number-theoretic transforms are developed. We show that fast algorithms applicable to ordinary NTT can also be used to compute the proposed FrNTT. Furthermore, we investigate the relationship between fractional Fourier and Hartley number-theoretic transforms, and demonstrate the applicability of the proposed FrNTT to a recently introduced image encryption scheme. |
| Databáze: | OpenAIRE |
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