Filtering of Nonuniformly Sampled Bandlimited Functions

The filtering of irregularly sampled bandlimited functions is discussed in this letter. An algorithm is given that enables the filtering of bandlimited functions with bandlimited filters to a desired precision, provided some requirements on the sampling density are met. All operations are carried ou...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 26; no. 7; pp. 1036 - 1040
Main Authors Huber, Adrian E. G., Liu, Shih-Chii
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Approximation algorithms
bandlimited functions
Convolution
Filtering
Filtration
Fourier transforms
Ground truth
Iterative methods
Jitter
Mathematical analysis
Matrix algebra
Matrix methods
Minimization
Nonuniform sampling
Signal processing algorithms
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Summary:The filtering of irregularly sampled bandlimited functions is discussed in this letter. An algorithm is given that enables the filtering of bandlimited functions with bandlimited filters to a desired precision, provided some requirements on the sampling density are met. All operations are carried out on the irregular samples themselves. The resulting algorithm is iterative in nature and converges quickly. It is also computationally tractable as it only requires matrix-vector multiplications. The algorithm is noncausal irrespective of the precise characteristics of the filter used, i.e., a buffer is necessary for implementation. The algorithm is evaluated on synthetic examples for which ground truth functions can be derived analytically.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2019.2918435