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研究生:蔡林忠
研究生(外文):Tsai, Lin Chung
論文名稱:利用改良式傳契法進行瞬時頻率估測
論文名稱(外文):Instantaneous Frequency Estimation with Modified Trench's Method
指導教授:陳巽璋
指導教授(外文):Chern, Shiunn Jang
學位類別:碩士
校院名稱:國立中山大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1994
畢業學年度:82
語文別:英文
論文頁數:45
中文關鍵詞:改良式傳契法波爾-范克定理主要特徵值
外文關鍵詞:modified Trench's methodBauer-Fike theoremprincipal eigenvalue
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在許多數位信號處理的應用上,估測信號的頻率是非常重要的問題。在本
論文,我們估測或追蹤含雜訊之信號頻率。 這個問題在震動的測量,都卜
勒雷達之信號,被動式聲納系統, 及語音信號之幅峰頻率(format
frequency)的估測等工程應用上深具重要性。 在本論文中, 我們使用前
向式線性預測濾波器(forward linear prediction filter)來發展一個新
的瞬時頻率估測方法。 在這新的方法中, 利用改良式傳契法(modified
Trench's method) 和波爾-范克定理(Bauer-Fike theorem) 去解赫米遜
(Hermitian)-拓普麗日(Toeplitz) 矩陣之主要的特徵值(eigenvalue)。
簡而言之, 剛開始收到 N 個資料後, 我們利用改良式傳契法去解矩陣之
主要的特徵值;當再收到新的資料時, 結合波爾-范克定理計算新的特徵值
。從模擬結果發現, 新的方法和用 QR 分解法來進行的結果接近, 尤其在
頻率 非常接近的時候; 在相同的情況下, 用傳統的適應性結構法所獲得
的結果則不令人滿意。除此之外, 這新方法的計算量較 QR 分解法要少,
尤其在並行處理的情況下。

The problem of estimating the frequency content of signals is
very important in many digital signal processing applications.
In this thesis, we are concerned with the problem of estimat-
ing and tracking the instantaneous frequency of the sinusoidal
signal together with additive white noise. Its solution has im-
portant applications in the fields of vibration measurements,
Doppler radar returns, passive sonar systems, and formant
frequency estimation of speech signals. In this thesis, a new
algorithm for IFE is developed. To do so, the forward linear
prediction filter is employed. In consequence, the modified
Trench's method along with the Bauer-Fike theorem is proposed
for solving the principal eigenvalues of the Hermitian Toepli-
tz autocorrelation matrix for instantaneous frequency estima-
tion (IFE).In fact,three kinds of eigenvalue searching schemes
can be employed in the modified Trench's method. In the new
algorithm for IFE, the modified Trench's method is first used
for solving the principal eigenvalues for initial block of
data with length N. When a new data is received,the Bauer-Fike
theorem is applied to search the new eigenvalues based on the
previous obtained eigenvalues.Such that the computational cost
can be reduced. The performance of the IFE using the presented
methodis compared with the conventional LMS adaptive method as
well as the QR based method. From the simulation results, we
found that the presented method can perform as good as the
QR based method, in terms of multiple frequencies estimation
where the frequencies are closer.But in the same situation the
conventional LMS adaptive method may not perform satisfacto-
rily. Moreover, the computational complexity of the presented
method is much less than QR based method, especially when the
presented method is implemented by the parallelized structure.

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