Traditional near-field antenna measurements use the sampling theorem to reconstruct the antenna pattern perfectly. However, a large number of measurement points are required for this approach. To address this problem, in this study, we propose a technique to accelerate the near-field antenna measurement, which is achieved by sparse E-field sampling in the region where the E-field changes smoothly and dense sampling in the region where the field changes rapidly. Further, our approach ensures robustness of measurement; the E-field information need not be known before carrying out measurements. Our experimental results demonstrate that our technique can reduce the number of measuring points by at least 64.9% when measuring two different patterns (15-GHz horn antenna with θ = 0° and 10°).

We survey some aspects of the classical prediction theory for stationary processes, in discrete time in Section 1, turning in Section 2 to continuous time, with particular reference to reproducing-kernel Hilbert spaces and the sampling theorem. We discuss the discrete-continuous theories of ARMA-CARMA, GARCH-COGARCH, and OPUC-COPUC in Section 3. We compare the various models treated in Section 4 by how well they model volatility, in particular volatility clustering. We discuss the infinite-dimensional case in Section 5, and turn briefly to applications in Section 6.

We consider and analyse sampling theories in the reproducing kernel Hilbert space (RKHS) in this paper. The reconstruction of a function in an RKHS from a given set of sampling points and the reproducing kernel of the RKHS is discussed. Firstly, we analyse and give the optimal approximation of any function belonging to the RKHS in detail. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding RKHS of complex-valued functions is investigated. Based on the derived results, another proof of the sampling theorem in the linear canonical transform (LCT) domain is given. Finally, the optimal approximation of any band-limited function in the LCT domain from infinite sampling points is also analysed and discussed.