Shannon-Type Sampling Theory on Unions of Equally Spaced and Noncommensurate Grids

Abstract

Sampling theory is that branch of mathematics that seeks to reconstruct functions from its values at a discrete set of points. The fundamental result in sampling theory known as "Shannon's sampling theorem" has many applications to signal processing and communications engineering. I demonstrate Shannon's result via complex interpolation methods. I then quote a result that uses these methods to solve interpolation problems on unions of noncommensurate lattices, which are created via a specific number of the- oretic guidelines. These interpolations give Shannon-type reconstructions on these lattices. I close by doing simulations in MATLAB of the sampling reconstructions on these noncommensurate grids.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2001
Accession Number
ADA387270

Entities

People

  • Terrence J. Moore

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Sensors

DTIC Thesaurus Topics

  • Complex Variables
  • Engineering
  • Fourier Analysis
  • Fourier Series
  • Image Processing
  • Information Science
  • Information Theory
  • Integrals
  • Interpolation
  • Mathematics
  • Multichannel
  • Numbers
  • Periodic Functions
  • Signal Processing
  • Simulations
  • Stochastic Processes
  • Theorems

Readers

  • Acoustical Oceanography.
  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space