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

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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4. 4. Papoulis, A. (1991) Probability, Random Variables, and Stochastic Processes, 3rd ed., McGraw-Hill, New York.
5. 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. 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. 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.