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Downsampling Non-Uniformly Sampled Data

Abstract

Decimating a uniformly sampled signal a factor D involves low-pass antialias filtering with normalized cutoff frequency 1/D followed by picking out every D th sample. Alternatively, decimation can be done in the frequency domain using the fast Fourier transform (FFT) algorithm, after zero-padding the signal and truncating the FFT. We outline three approaches to decimate non-uniformly sampled signals, which are all based on interpolation. The interpolation is done in different domains, and the inter-sample behavior does not need to be known. The first one interpolates the signal to a uniformly sampling, after which standard decimation can be applied. The second one interpolates a continuous-time convolution integral, that implements the antialias filter, after which every D th sample can be picked out. The third frequency domain approach computes an approximate Fourier transform, after which truncation and IFFT give the desired result. Simulations indicate that the second approach is particularly useful. A thorough analysis is therefore performed for this case, using the assumption that the non-uniformly distributed sampling instants are generated by a stochastic process.

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Correspondence to Fredrik Gustafsson.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Eng, F., Gustafsson, F. Downsampling Non-Uniformly Sampled Data. EURASIP J. Adv. Signal Process. 2008, 147407 (2007). https://doi.org/10.1155/2008/147407

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  • DOI: https://doi.org/10.1155/2008/147407

Keywords

  • Fourier
  • Fourier Transform
  • Information Technology
  • Stochastic Process
  • Convolution