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AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE

Year 2019, Volume: 24 Issue: 2, 419 - 428, 30.08.2019

Betofe Mboyo Keyta Sevim Hazal Uz Erdoğan Dilaveroğlu

https://doi.org/10.17482/uumfd.559986

Abstract

The
k-PHD method, a generalization of the well-known Pisarenko harmonic
decomposition (PHD) method, is considered for frequency estimation of a single
real random-phased sinusoid in noise. With the use of a simple variance
analysis technique, an exact expression of the k-PHD frequency variance is
derived. An approximate k-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 PHD method k-PHD method Variance analysis

References

  • 1. Chan, K. W. and So, H. C. (2003) An exact analysis of Pisarenko’s single-tone frequency estimation algorithm, Signal Processing, 83(3), 685-690. doi: 10.1016/S0165-1684(02)00493-0
  • 2. De Sabata, A., Toma, L., and Mischie, S. (2007) A new two-step single tone frequency estimation algorithm, International Journal of Circuits, Systems and Signal Processing, 2(1), 105-108.
  • 3. Keyta, B. M. and Dilaveroğlu, E. (2019) An exact variance expression of Pisarenko’s method for frequency estimation of a single real sinusoid: Random Phase Case, 3rd International Symposium on Innovative Approaches in Scientific Studies, Ankara, Turkey, 4(1), 533-536.
  • 4. Papoulis, A. (1991) Probability, Random Variables, and Stochastic Processes, 3rd ed., McGraw-Hill, New York.
  • 5. Sakai, H: (1984) Statistical analysis of Pisarenko’s method for sinusoidal frequency estimation, IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(1), 95-101.
  • 6. So, H. C., Chan, Y. T., Ho, K. C., and Chen, Y. (2013) Simple formulas for bias and mean square error computation, IEEE Signal Processing Magazine, 30(4), 162-165. doi: 10.1109/MSP.2013.2254600
  • 7. Toma, L., De Sabata, A. and Vasiu, G. (2007) Two-step procedure decreases variance in tone frequency estimation, Revue Roumaine des Sciences Techniques, Serie Électrotechnique et Énergetique, 52(4), 463-474.
  • 8. Uz, S. H. and Dilaveroğlu, E. (2019) Simple and accurate bias and variance expressions of some instantaneous frequency estimators including the DESAs, 3rd International Symposium on Innovative Approaches in Scientific Studies, Ankara, Turkey, 4(1), 537-540.

k-PHD Tek-Ton Frekans Kestiricisinin Bir Kesin Değişinti İfadesi: Rasgele Faz Durumu

Year 2019, Volume: 24 Issue: 2, 419 - 428, 30.08.2019

Betofe Mboyo Keyta Sevim Hazal Uz Erdoğan Dilaveroğlu

https://doi.org/10.17482/uumfd.559986

Abstract

İyi
bilinen Pisarenko harmonik ayrışım (PHD) metodunun bir genelleştirilmesi olan
k-PHD metodu gürültü içindeki bir reel rasgele fazlı sinüsün frekans kestirimi
için ele alınmıştır. Basit bir değişinti analiz tekniği kullanılarak, k-PHD
frekans değişintisinin bir kesin ifadesi çıkarılmıştır. Yeteri kadar geniş veri
uzunlukları ve yüksek işaret gürültü oranları için bir yaklaşık k-PHD değişinti
formülü de verilmektedir. Kuramsal sonuçları teyit eden bilgisayar benzetimleri
dâhil edilmiştir.

Keywords

Frekans kestirimi Reel sinus PHD metodu k-PHD metodu Değişinti analizi

References

  • 1. Chan, K. W. and So, H. C. (2003) An exact analysis of Pisarenko’s single-tone frequency estimation algorithm, Signal Processing, 83(3), 685-690. doi: 10.1016/S0165-1684(02)00493-0
  • 2. De Sabata, A., Toma, L., and Mischie, S. (2007) A new two-step single tone frequency estimation algorithm, International Journal of Circuits, Systems and Signal Processing, 2(1), 105-108.
  • 3. Keyta, B. M. and Dilaveroğlu, E. (2019) An exact variance expression of Pisarenko’s method for frequency estimation of a single real sinusoid: Random Phase Case, 3rd International Symposium on Innovative Approaches in Scientific Studies, Ankara, Turkey, 4(1), 533-536.
  • 4. Papoulis, A. (1991) Probability, Random Variables, and Stochastic Processes, 3rd ed., McGraw-Hill, New York.
  • 5. Sakai, H: (1984) Statistical analysis of Pisarenko’s method for sinusoidal frequency estimation, IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(1), 95-101.
  • 6. So, H. C., Chan, Y. T., Ho, K. C., and Chen, Y. (2013) Simple formulas for bias and mean square error computation, IEEE Signal Processing Magazine, 30(4), 162-165. doi: 10.1109/MSP.2013.2254600
  • 7. Toma, L., De Sabata, A. and Vasiu, G. (2007) Two-step procedure decreases variance in tone frequency estimation, Revue Roumaine des Sciences Techniques, Serie Électrotechnique et Énergetique, 52(4), 463-474.
  • 8. Uz, S. H. and Dilaveroğlu, E. (2019) Simple and accurate bias and variance expressions of some instantaneous frequency estimators including the DESAs, 3rd International Symposium on Innovative Approaches in Scientific Studies, Ankara, Turkey, 4(1), 537-540.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Betofe Mboyo Keyta This is me

Sevim Hazal Uz This is me

Erdoğan Dilaveroğlu 0000-0002-8432-623X

Publication Date August 30, 2019
Submission Date May 2, 2019
Acceptance Date June 10, 2019
Published in Issue Year 2019 Volume: 24 Issue: 2

Cite

APA Keyta, B. M., Uz, S. H., & Dilaveroğlu, E. (2019). AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 24(2), 419-428. https://doi.org/10.17482/uumfd.559986
AMA Keyta BM, Uz SH, Dilaveroğlu E. AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. UUJFE. August 2019;24(2):419-428. doi:10.17482/uumfd.559986
Chicago Keyta, Betofe Mboyo, Sevim Hazal Uz, and Erdoğan Dilaveroğlu. “AN EXACT VARIANCE EXPRESSION OF THE K-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 24, no. 2 (August 2019): 419-28. https://doi.org/10.17482/uumfd.559986.
EndNote Keyta BM, Uz SH, Dilaveroğlu E (August 1, 2019) AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 24 2 419–428.
IEEE B. M. Keyta, S. H. Uz, and E. Dilaveroğlu, “AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE”, UUJFE, vol. 24, no. 2, pp. 419–428, 2019, doi: 10.17482/uumfd.559986.
ISNAD Keyta, Betofe Mboyo et al. “AN EXACT VARIANCE EXPRESSION OF THE K-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi 24/2 (August 2019), 419-428. https://doi.org/10.17482/uumfd.559986.
JAMA Keyta BM, Uz SH, Dilaveroğlu E. AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. UUJFE. 2019;24:419–428.
MLA Keyta, Betofe Mboyo et al. “AN EXACT VARIANCE EXPRESSION OF THE K-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, vol. 24, no. 2, 2019, pp. 419-28, doi:10.17482/uumfd.559986.
Vancouver Keyta BM, Uz SH, Dilaveroğlu E. AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. UUJFE. 2019;24(2):419-28.

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