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

Yıl 2019, Cilt: 24 Sayı: 2, 419 - 428, 30.08.2019

Betofe Mboyo Keyta Sevim Hazal Uz Erdoğan Dilaveroğlu

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

Öz

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.

Anahtar Kelimeler

Frequency estimation, Real sinusoid, PHD method, k-PHD method, Variance analysis

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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• 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.
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• 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.