系數(shù)矩陣正交矢量譜估計
NEW SPECTRAL ESTIMATION APPROACHES IN LPEF COEFFICIENT MATRIX SPACE
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摘要: 鄒理和(1984)提出,用線性預(yù)測誤差濾波器系數(shù)矩陣對K個二維復(fù)正弦波加白噪聲的信號作譜估計,有著良好的特性。本文將證明,二維線性預(yù)測誤差濾波器系數(shù)矩陣空間具有和相關(guān)陣空間非常類似的結(jié)構(gòu)。在系數(shù)陣空間同樣存在正交矢量譜估計方法。采用相關(guān)陣SVD逼近技術(shù),可使系數(shù)陣正交矢量方法不僅具有很高分辨率,而且具有很好的統(tǒng)計穩(wěn)定性。最后將二維的結(jié)果移植到一維,并在一維中進行了計算機模擬,模擬結(jié)果表明新方法比現(xiàn)用的一些方法為佳。
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關(guān)鍵詞:
- 信號處理; 線性預(yù)測誤差濾波器; 正交矢量譜估計
Abstract: For the case of sinusoids plus white noise, it will be proved that the construction of the LPEF (Linear Prediction Error Filter) coefficient matrix space is quite similar to that of the correlation matrix space. Therefore, the orthogonal vector techniques can be applied to the LPEF coefficient matrix space for spectral estimation. With the SVD approximation approach used for the correlation matrix, the present approach has not only the property of high resolution, but also the property of high statistic stability. finally, a one dimensional LPEF coefficient matrix is formed and the spectral estimation is simulated by computer. The results are compared with those obtained by other approaches. -
Li He Zou(鄒理和) On Resolution of 2-D Spectral Estimation as Applied to Sinusoids in White Noise,Ph. D. Dissertation, Princeton University, 1984.[2]S.M. Kay, S. L. Marple, Jr. PIEE, 69(1981), 1380-1419.[3]G. Bienvenu, Eigensystem Properties of Sampled Space Coherent Signal and Interference, Proc. ICASSP,1984.[4]T.K.Citron, T. Kailath, An Improved Eigenvector Beamformer, Proc. ICASSP, 1984.Angzhao Di, L.Tiao, Matrix Decomposition and Multiple Source Location, Proc. ICASSP, 1984.[5]D. W. Tufts, R. Kumaresan, Proc. IEEE, 70(1982), 975-989.[6]O. I. Frost, Power Spectrum Estimation, In 1976 NATO Advanced Study Institute on Signal Processing with Emphasis on Underwater Acoustic Portovence, Italy, 1976.[7]H.C. Lin, Trans, IEEE on AP, AP-30(1982).[8]D. R. Farrier, PIEE, 131(1984).[9]C. L. Lawson, R.J. Hanson, Solving Least Squares Problems, Englewood Cliffs, NJ, Prentice Hall, 1974. -
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