A computable fourier condition generating alias-free sampling lattices

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1768-1782
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume57
Issue number5
DOIs
StatePublished - 2009

Keywords

  • Critical sampling
  • Densest sampling
  • Divergence theorem
  • Fourier transforms of indicator functions
  • Maximal decimation
  • Nonredundant filter banks
  • Optimal sampling
  • Packing
  • Poisson summation formula
  • Tiling

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Fingerprint Dive into the research topics of 'A computable fourier condition generating alias-free sampling lattices'. Together they form a unique fingerprint.

Cite this