A Fast Fourier Transform with Rectangular Output on the BCC and FCC Lattices
نویسندگان
چکیده
This paper discusses the efficient, non-redundant evaluation of a Discrete Fourier Transform on the three dimensional Body-Centered and Face-Centered Cubic lattices. The key idea is to use an axis aligned window to truncate and periodize the sampled function which leads to separable transforms. We exploit the geometry of these lattices and show that by choosing a suitable non-redundant rectangular region in the frequency domain, the transforms can be efficiently evaluated using the Fast Fourier Transform.
منابع مشابه
Pass-Band Optimal Reconstruction on the Body-Centered Cubic Lattice
In this paper, a pass-band optimal reconstruction technique is adapted to the Body-Centered Cubic (BCC) lattice. In order to perform the frequencydomain preprocessing, we derive a practical Discrete Fourier Transform (DFT) for BCC-sampled data. In the discrete frequency domain our DFT provides a natural isotropic periodicity on a FaceCentered Cubic (FCC) pattern, unlike the previous method, whi...
متن کاملOptimal Sampling Lattices and Trivariate Box Splines
The Body Centered Cubic (BCe) and Face Centered Cubic (FCC) lattices along with a set of box splines for sampling and reconstruction of trivariate functions are proposed. The BCC lattice is demonstrated to be the optimal choice of a pattern for generic sampling purposes. While the FCC lattice is the second best choice for this purpose, both FCC and BCC lattices significantly outperform the accu...
متن کاملData Processing on the Body - Centered Cubic Lattice
The body-centered cubic (BCC) lattice is the optimal three-dimensional sampling lattice. Its optimality stems from the fact that its dual, the face-centered cubic (FCC) lattice, achieves the highest sphere-packing efficiency. In order to approximate a scalar-valued function from samples that reside on a BCC lattice, spline-like compact kernels have been recently proposed. The lattice translates...
متن کاملOccasional ‘‘long-range’’ nonequilibrium body-centered-cubic structures in NiFe/Cu spin valves
We describe conventional and high-resolution transmission electron microscopy ~HRTEM! characterization of the microstructure of sputtered NiFe/Cu giant magnetoresistance spin valves ~Cu/FeMn/NiFe/Cu/NiFe! sandwiched between thick Nb contact layers. Six spin valves, sputtered at different temperatures, three with thin ~3 nm! and three with thick ~24 and 30 nm! NiFe layers, were studied. All of t...
متن کاملCalibration of the Marschner-Lobb Signal on CC, BCC, and FCC Lattices
The well-known Marschner-Lobb (ML) signal has been originally proposed for visually comparing 3D resampling filters applied on the traditional Cartesian Cubic (CC) lattice. Recently, this popular benchmark is also used for evaluating reconstruction schemes designed for the optimal Body-Centered Cubic (BCC) lattice and the suboptimal Face-Centered Cubic (FCC) lattice. Nevertheless, to the best o...
متن کامل