Optimal random sampling for spectrum estimation in DASP applications

Andrzej Tarczynski; Dongdong Qu

International Journal of Applied Mathematics and Computer Science (2005)

  • Volume: 15, Issue: 4, page 463-469
  • ISSN: 1641-876X

Abstract

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In this paper we analyse a class of DASP (Digital Alias-free Signal Processing) methods for spectrum estimation of sampled signals. These methods consist in sampling the processed signals at randomly selected time instants. We construct estimators of Fourier transforms of the analysed signals. The estimators are unbiased inside arbitrarily wide frequency ranges, regardless of how sparsely the signal samples are collected. In order to facilitate quality assessment of the estimators, we calculate their standard deviations. The optimal sampling scheme that minimises the variance of the resulting estimator is derived. The further analysis presented in this paper shows how sampling instant jitter deteriorates the quality of spectrum estimation. A couple of numerical examples illustrate the main thesis of the paper.

How to cite

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Tarczynski, Andrzej, and Qu, Dongdong. "Optimal random sampling for spectrum estimation in DASP applications." International Journal of Applied Mathematics and Computer Science 15.4 (2005): 463-469. <http://eudml.org/doc/207758>.

@article{Tarczynski2005,
abstract = {In this paper we analyse a class of DASP (Digital Alias-free Signal Processing) methods for spectrum estimation of sampled signals. These methods consist in sampling the processed signals at randomly selected time instants. We construct estimators of Fourier transforms of the analysed signals. The estimators are unbiased inside arbitrarily wide frequency ranges, regardless of how sparsely the signal samples are collected. In order to facilitate quality assessment of the estimators, we calculate their standard deviations. The optimal sampling scheme that minimises the variance of the resulting estimator is derived. The further analysis presented in this paper shows how sampling instant jitter deteriorates the quality of spectrum estimation. A couple of numerical examples illustrate the main thesis of the paper.},
author = {Tarczynski, Andrzej, Qu, Dongdong},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {random sampling; optimal sampling; spectral analysis; digital alias-free signal processing},
language = {eng},
number = {4},
pages = {463-469},
title = {Optimal random sampling for spectrum estimation in DASP applications},
url = {http://eudml.org/doc/207758},
volume = {15},
year = {2005},
}

TY - JOUR
AU - Tarczynski, Andrzej
AU - Qu, Dongdong
TI - Optimal random sampling for spectrum estimation in DASP applications
JO - International Journal of Applied Mathematics and Computer Science
PY - 2005
VL - 15
IS - 4
SP - 463
EP - 469
AB - In this paper we analyse a class of DASP (Digital Alias-free Signal Processing) methods for spectrum estimation of sampled signals. These methods consist in sampling the processed signals at randomly selected time instants. We construct estimators of Fourier transforms of the analysed signals. The estimators are unbiased inside arbitrarily wide frequency ranges, regardless of how sparsely the signal samples are collected. In order to facilitate quality assessment of the estimators, we calculate their standard deviations. The optimal sampling scheme that minimises the variance of the resulting estimator is derived. The further analysis presented in this paper shows how sampling instant jitter deteriorates the quality of spectrum estimation. A couple of numerical examples illustrate the main thesis of the paper.
LA - eng
KW - random sampling; optimal sampling; spectral analysis; digital alias-free signal processing
UR - http://eudml.org/doc/207758
ER -

References

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