Quaternion Fourier Transform on Quaternion Fields and Generalizations
Quaternion Fourier Transform on Quaternion Fields and Generalizations
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DOI：
10.1007/s00006-007-0037-8
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发表时间：
2007-05
影响因子：
1.5
通讯作者：
E. Hitzer
中科院分区：
文献类型：
--
作者：
E. Hitzer
我们将四元数傅里叶变换（QFT）应用于四元数域，并研究了QFT的应用性质。不同形式的QFT导致我们不同的Plancherel定理。我们将四元数场的QFT计算与真实的信号的QFT计算联系起来。我们用矩阵、Clifford几何代数和例子研究了QFT的一般线性变换行为。我们最终到达广泛的非交换多向量FT推广的QFT。给出的例子是新的体积时间和时空代数傅立叶变换。
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.