Quaternion Fourier Transform on Quaternion Fields and Generalizations
نویسنده
چکیده
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. Mathematics Subject Classification (2000). Primary 42A38; Secondary 11R52.
منابع مشابه
Quaternion Fourier Transform for Colour Images
The Fourier transforms plays a critical role in broad range of image processing applications, including enhancement, restoration, analysis and compression. For filtering of gray scale images 2D Fourier transform is an important tool which converts the image from spatial domain to frequency domain and then by applying filtering mask filtering is done. To filter color images, a new approach is im...
متن کاملOPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f ,g, or by only one pure unit quaternion f , comment on their geometric meaning, and establish invers...
متن کاملTwo-dimensional quaternion wavelet transform
In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...
متن کاملGeneralized Sampling Expansions Associated with Quaternion Fourier Transform
Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a σ-bandli...
متن کاملQuaternion Algebra-Valued Wavelet Transform
The quaternion Fourier transform (QFT), which is a nontrivial generalization of the real and complex Fourier transform (FT) using quaternion algebra has been of interest to researchers for some years (see e.g. [3, 5]). It was found that many FT properties still hold but others have to be modified. Based on the (right-sided) QFT, one can extend the classical wavelet transform (WT) to quaternion ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1306.1023 شماره
صفحات -
تاریخ انتشار 2013