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2005 | 15 | 4 | 463-469
Tytuł artykułu

Optimal random sampling for spectrum estimation in DASP applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
15
Numer
4
Strony
463-469
Opis fizyczny
Daty
wydano
2005
otrzymano
2005-06-01
poprawiono
2005-09-01
Twórcy
  • Department of Electronic Systems, University of Westminster, 115 New Cavendish Street, London, W1W 6UW, UK
autor
  • Department of Electronic Systems, University of Westminster, 115 New Cavendish Street, London, W1W 6UW, UK
Bibliografia
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  • Landau H.J. (1967): Necessary density conditions for sampling and interpolation of certain entire functions. - Acta Math., Vol. 117, pp. 37-52.
  • Lomb N.R. (1976): Least-squares frequency analysis of unequally spaced data. - Astroph. Space Sc., Vol. 39, No. 2, pp. 447-462.
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  • Scargle J.D. (1982): Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. - Astronom. J., Vol. 263, No. 1, pp. 835-853.
  • Scargle J.D. (1989): Studies in astronomical time series analysis. III. Fourier transforms, autocorrelation functions, and gross-correlation functions of unevenly spaced data. - Astronom. J., Vol. 343, No. 1, pp. 874-887.
  • Shapiro H.S. and Silverman R.A. (1960): Alias-free sampling of random noise. - SIAM J. Appl. Math., Vol. 8, No. 2, pp. 225-236.
  • Tarczyński A. (1997): Sensitivity of signal reconstruction. - IEEE Signal Process. Lett., Vol. 4, No. 7, pp. 192-194.
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  • Tarczyński A. and Cain G.D. (1997): Reliability of signal reconstruction from finite sets of samples. - 1997 Workshop Sampling Theory and Applications, SAMPTA'97, Aveiro, Portugal, Vol. 1, pp. 181-186.
  • Tarczyński A. and Valimaki V. (1996): Modifying FIR and IIR filters for processing signals with lost samples. - Proc. IEEE Nordic Signal ProcessingSymposium, NORSIG'96, Helsinki, Finland, Vol. 1, pp. 359-362.
  • Tarczyński A., Valimaki V. and Cain G.D. (1997): FIR filtering of nonuniformly sampled signals. - IEEE Int. Conf. Acoustics, Speech and Signal Processing, ICASSP'97, Munich, Germany, Vol. 3, pp. 2237-2240.
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