2-Dimensional Quaternionic Fourier Transform and Applications
In this work, we define the Two-dimensional (left) Quaternion Fourier Transform (2D-QFT) of f ∈ L1 (R2; H), which is the function Fq{ f } : R2 → H defined by Fq{ f }(ω) = ̂ f (ω) =∫R2 e−μω·x f (x)d2x, where x = x1e1 + x2e2, ω = ω1e1 + ω2e2, with quaternion Fourier kernel e−μω·x such that |μ| = 1. We...
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| Format: | bachelorThesis |
| Idioma: | eng |
| Publicat: |
2022
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| Matèries: | |
| Accés en línia: | http://repositorio.yachaytech.edu.ec/handle/123456789/521 |
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Afegir etiqueta | Sumari: | In this work, we define the Two-dimensional (left) Quaternion Fourier Transform (2D-QFT) of f ∈ L1 (R2; H), which is the function Fq{ f } : R2 → H defined by Fq{ f }(ω) = ̂ f (ω) =∫R2 e−μω·x f (x)d2x, where x = x1e1 + x2e2, ω = ω1e1 + ω2e2, with quaternion Fourier kernel e−μω·x such that |μ| = 1. We derive the shift, modulation, and convolution properties and estab-lish the Plancherel and vector differential theorem. Furthermore, we will study the application of this Fourier transform to the resolution to the heat equation. |
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