Ten lectures on wavelets
Multirate systems and filter banks
Multirate systems and filter banks
Wavelets and subband coding
Densest translational lattice packing of non-convex polygons (extended abstract)
Proceedings of the sixteenth annual symposium on Computational geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Densest lattice packings of 3-polytopes
Computational Geometry: Theory and Applications
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
IEEE Transactions on Visualization and Computer Graphics
The Plenacoustic Function and Its Sampling
IEEE Transactions on Signal Processing
Multiresolution direction filterbanks: theory, design, and applications
IEEE Transactions on Signal Processing - Part I
IEEE Transactions on Information Theory
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Multidimensional Directional Filter Banks and Surfacelets
IEEE Transactions on Image Processing
IEEE Transactions on Signal Processing
Hi-index | 35.69 |
We propose a Fourier analytical condition linking alias-free sampling with the Fourier transform of the indicator function defined on the given frequency support. Our discussions center around how to develop practical computation algorithms based on the proposed analytical condition. We address several issues along this line, including the derivation of simple closed-form expressions for the Fourier transforms of the indicator functions defined on arbitrary polygonal and polyhedral domains; a complete and nonredundant enumeration of all quantized sampling lattices via the Hermite normal forms of integer matrices; and a quantitative analysis of the approximation of the original infinite Fourier condition by using finite computations. Combining these results, we propose a computational testing procedure that can efficiently search for the optimal alias-free sampling lattices for a given polygonal or polyhedral shaped frequency domain. Several examples are presented to show the potential of the proposed algorithm in multidimensional filter bank design, as well as in applications involving the design of efficient sampling patterns for multidimensional band-limited signals.