Sampling and approximation of bandlimited volumetric data

Rami Katz, Yoel Shkolnisky*

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review

2 Scopus citations


We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is based on expanding the given function in the basis of generalized prolate spheroidal wavefunctions, with the expansion coefficients given by weighted dot products between the samples of the function and the samples of the basis functions. As numerical implementations require all expansions to be finite, we present a truncation rule for the expansions. Finally, we derive a bound on the overall approximation error in terms of the assumed space/frequency concentration.

Original languageEnglish
Pages (from-to)235-247
Number of pages13
JournalApplied and Computational Harmonic Analysis
Issue number1
StatePublished - Jul 2019


FundersFunder number
National Institute of General Medical Sciences
Horizon 2020 Framework ProgrammeR01GM090200, 723991
European Research Council


    • Bandlimited approximation
    • Bandlimited functions
    • Prolate spheroidal wave functions


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