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Everything about Multidimensional sampling
In digital signal processing, multidimensional sampling is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton on conditions for perfectly reconstructing a wavenumber-limited function from its measurements on a discrete lattice of points. This result, also known as the Petersen–Middleton theorem, is a generalization of the Nyquist–Shannon sampling theorem for sampling one-dimensional band-limited functions to higher-dimensional Euclidean spaces. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Multidimensional samplingA 5-minute orientation
- Skim a recent paper: Multidimensional Kantorovich modifications of exponential sampling seriesInfluential work since 2022
- Pick up a classic book: The Analysis Of Survey DataThe most-reprinted book on the subject
- Read the landmark paper: Latin hypercube sampling with multidimensional uniformityCited 162 times
- Go sideways: LPBoostA closely related topic
- Go sideways: Lindelöf's theoremA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Latin hypercube sampling with multidimensional uniformity
Time-resolved multidimensional NMR with non-uniform sampling
Nonuniform Sampling and Maximum Entropy Reconstruction in Multidimensional NMR
Multidimensional adaptive sampling and reconstruction for ray tracing
Random sampling in multidimensional NMR spectroscopy
Optimization of random time domain sampling in multidimensional NMR
Recursive Stratified Sampling for Multidimensional Monte Carlo Integration
Efficient Multidimensional Sampling
🆕 Influential since 2022
Multidimensional Kantorovich modifications of exponential sampling series
Full population testing: Applying multidimensional audit data sampling (MADS) to general ledger data auditing
Optimal sampling designs for multidimensional streaming time series with application to power grid sensor data
A multidimensional discrete sampling method for deriving regional level seismic fragility and losses of RC existing buildings
Computational textural mapping harmonises sampling variation and reveals multidimensional histopathological fingerprints
📚 Books worth reading
The Analysis Of Survey DataColm A. O'Muircheartaigh, Clive Payne · 1977
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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