Yıl 2019, Cilt 24 , Sayı 2, Sayfalar 419 - 428 2019-08-30

k-PHD Tek-Ton Frekans Kestiricisinin Bir Kesin Değişinti İfadesi: Rasgele Faz Durumu
AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE

Betofe Mboyo KEYTA [1] , Sevim Hazal UZ [2] , Erdoğan DİLAVEROĞLU [3]


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.

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.

  • 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.
Birincil Dil en
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Yazar: Betofe Mboyo KEYTA
Kurum: Bursa Uludağ Üniversitesi

Yazar: Sevim Hazal UZ
Kurum: Bursa Uludağ Üniversitesi

Orcid: 0000-0002-8432-623X
Yazar: Erdoğan DİLAVEROĞLU (Sorumlu Yazar)
Kurum: Bursa Uludağ Üniversitesi
Ülke: Turkey


Tarihler

Başvuru Tarihi : 2 Mayıs 2019
Kabul Tarihi : 10 Haziran 2019
Yayımlanma Tarihi : 30 Ağustos 2019

Bibtex @araştırma makalesi { uumfd559986, journal = {Uludağ University Journal of The Faculty of Engineering}, issn = {2148-4147}, eissn = {2148-4155}, address = {}, publisher = {Bursa Uludağ Üniversitesi}, year = {2019}, volume = {24}, pages = {419 - 428}, doi = {10.17482/uumfd.559986}, title = {AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE}, key = {cite}, author = {KEYTA, Betofe Mboyo and UZ, Sevim Hazal and DİLAVEROĞLU, Erdoğan} }
APA KEYTA, B , UZ, S , DİLAVEROĞLU, E . (2019). AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. Uludağ University Journal of The Faculty of Engineering , 24 (2) , 419-428 . DOI: 10.17482/uumfd.559986
MLA KEYTA, B , UZ, S , DİLAVEROĞLU, E . "AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE". Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 419-428 <https://dergipark.org.tr/tr/pub/uumfd/issue/45830/559986>
Chicago KEYTA, B , UZ, S , DİLAVEROĞLU, E . "AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE". Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 419-428
RIS TY - JOUR T1 - AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE AU - Betofe Mboyo KEYTA , Sevim Hazal UZ , Erdoğan DİLAVEROĞLU Y1 - 2019 PY - 2019 N1 - doi: 10.17482/uumfd.559986 DO - 10.17482/uumfd.559986 T2 - Uludağ University Journal of The Faculty of Engineering JF - Journal JO - JOR SP - 419 EP - 428 VL - 24 IS - 2 SN - 2148-4147-2148-4155 M3 - doi: 10.17482/uumfd.559986 UR - https://doi.org/10.17482/uumfd.559986 Y2 - 2019 ER -
EndNote %0 Uludağ University Journal of The Faculty of Engineering AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE %A Betofe Mboyo KEYTA , Sevim Hazal UZ , Erdoğan DİLAVEROĞLU %T AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE %D 2019 %J Uludağ University Journal of The Faculty of Engineering %P 2148-4147-2148-4155 %V 24 %N 2 %R doi: 10.17482/uumfd.559986 %U 10.17482/uumfd.559986
ISNAD KEYTA, Betofe Mboyo , UZ, Sevim Hazal , DİLAVEROĞLU, Erdoğan . "AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE". Uludağ University Journal of The Faculty of Engineering 24 / 2 (Ağustos 2019): 419-428 . https://doi.org/10.17482/uumfd.559986
AMA KEYTA B , UZ S , DİLAVEROĞLU E . AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. JFE. 2019; 24(2): 419-428.
Vancouver KEYTA B , UZ S , DİLAVEROĞLU E . AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE. Uludağ University Journal of The Faculty of Engineering. 2019; 24(2): 428-419.