We use the recent comprehensive research [17, 19] on the manifolds of square roots of −1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j ∈ C is replaced by a square root of−1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known ...

High-efficiency video coding (HEVC) is a new video coding standard being developed by the Joint Collaborative Team on Video Coding. HEVC adopted numerous new tools, such as more flexible data structure representations, which include the coding unit (CU), prediction unit, and transform unit. In the partitioning of the largest coding unit (LCU) into CUs, rate distortion optimization (RDO) is appl...

Closed-form solutions have been derived for the diffraction patterns at the focal plane of (1) a convergent wave of unit amplitude illuminating a segment of a circular aperture and (2) a convergent wave of Gaussian amplitude diffracted by an infinite edge. Photographs showing the main features of these edge transform patterns are presented together with computer-generated graphs.

Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate coefficient estimates, distortion bounds and the results on integral transform. Further we investigate the neighbourhood results and partial sums. 2000 Mathematics Subject Classification: 30C45.

Severe phenomena of across range-Doppler unit (ARDU) and decoherence occur when radar detects high-speed high-maneuvering targets, causing degradation in detection performance traditional FFT methods. The improvement resolution causes a multi-dimensional spread phenomenon, where different scattering centers the target are distributed on range units, along with motion parameters such as velocity...

In this paper we present a systematic approach to applying expressive performance models to non-expressive score transcriptions and synthesizing the results by means of concatenative synthesis. Expressive performance models are built from score transcriptions and recorded performances by means of decision tree rule induction, and those models are used both to transform inexpressive input scores...

We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball B of C. The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Mathematics Subject Classification (2000). Primary 47A57; Secondary 30E05.

We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this purpose we study in detail the properties of the restriction of Fourier transform on the unit cotangent sphere associated with the symbols of multipliers.