An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case Betofe Mboyo Keyta 1, Erdoğan Dilaveroğlu 2* 1Bursa Uludağ University , Bursa , Turkey 2Bursa Uludağ University , Bursa , Turkey
IEEE B. Keyta , E. Dilaveroğlu , "An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case", SETSCI Conference Proceedings, vol. 4, pp. 533-536, 2019.
BibTeX
@INPROCEEDINGS{citation,
author = {Keyta , Betofe Mboyo and Dilaveroğlu , Erdoğan },
title = {An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case},
year = {2019},
volume = {4},
pages = {533-536},
publisher = {SETSCI Conference Proceedings},
abstract = {Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development},
doi = {},
}
RIS
TY - CONF
AU - Keyta , Betofe Mboyo
AU - Dilaveroğlu , Erdoğan
TI - An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case
PY - 2019
PB - SETSCI Conference Proceedings
VL - 4
AB - Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development
DO -
ER -
EndNote
%0 Book
%A Keyta , Betofe Mboyo
%A Dilaveroğlu , Erdoğan
%T An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case
%D 2019
%I {SETSCI Conference Proceedings}
%J {SETSCI Conference Proceedings}
%V 4
%P 533-536
%D 2019
%M doi:
Open Access
An Exact Variance Expression of Pisarenko’s Method for Frequency Estimation of a Single Real Sinusoid: Random Phase Case
Betofe Mboyo Keyta 1, Erdoğan Dilaveroğlu 2* 1Bursa Uludağ University , Bursa , Turkey 2Bursa Uludağ University , Bursa , Turkey * Corresponding author: dilaver@uludag.edu.tr
Several statistical analyses of the Pisarenko harmonic decomposition (PHD) method for frequency estimation of a single real sinusoid in noise have been carried out in the literature. However, all of the analyses consider the phase of the sinusoid as a constant parameter which does not change from one snapshot to another. In this paper, it is assumed that the phase is a random variable uniformly distributed in an interval of length 2 . With the use of a simple variance analysis technique, an exact expression of the PHD frequency variance is derived. An approximate PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development
Keywords - Frequency estimation; Real sinusoid; Pisarenko’s method; Variance analysis
[1] H. Sakai, “Statistical analysis of Pisarenko’s method for sinusoidal frequency estimation,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 1, pp. 95-101, February 1984.
[2] K. W. Chan and H. C. So, “An exact analysis of Pisarenko’s singletone frequency estimation algorithm,” Signal Processing, vol. 83, no.3, pp. 685-690, March 2003.
[3] H. C. So, Y. T. Chan, K. C. Ho, and Yuan Chen, “Simple formulas for bias and mean square error computation,” IEEE Signal Processing Magazine, vol. 30, no. 4, pp. 162-165, July 2013.
[4] A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed., New York: McGraw-Hill, 1991.
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