瞬時頻率在信號分析與估測上的兩個應用

Two Applications of Instantaneous Frequency to Signal Analysis and Estimation

馬萬軍(Wann-Jiun Ma)

指導教授 ： 張帆人

共同指導教授 ： 唐望

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.00302

摘要

本論文提出瞬時頻率在信號分析與信號估測上的兩個應用。第一個應用是分析名為復古現象的飛行載具縱向長周期振動。在此處，提出利用一個希爾伯特-黃轉換(HHT)來分析此時域上的物理測量數據。這個方法是以稱為經驗模態分解(EMD)的方式產生一組本質模態函數(IMF)為基礎。HHT適用於非穩態與非線性的數據分析，及找出數據包括頻率的瞬時特性是其的主要概念。此外，結合快速傅利業轉換(FFT)與EMD呈現出與HHT不同的結果。在復古的分析中，利用實際動態GPS測量所得的飛行數據，我們呈現出非穩態信號分析(HHT)和傳統以傅利業為基礎之方法的比較。

在本論文的第二個部分，我們提出一個利用適應性全通帶式凹谷濾波器(ANFA)搭配上高斯-牛頓演算法作為GPS抗窄頻干擾系統的應用。在模擬中考慮了穩態及非穩態的干擾。ANFA可以即時的估測干擾的瞬時頻率且它比傳統的時域適應預估器有較好的均方預估誤差(MSPE)與信號雜訊改善率(SNR)。

關鍵字

瞬時頻率 ； 希爾伯特-黃轉換 ； 經驗模態分解 ； 本質模態函數 ； 復古 ； 全球定位系統 ； 適應性全通帶式凹谷濾波器 ； 高斯-牛頓演算法 ； 抗窄頻干擾

並列摘要

This thesis deals with two applications of instantaneous frequency to signal analysis and estimation. The first application is the analysis of aircraft longitudinal long-period oscillation named phugoid phenomenon. A Hilbert-Huang Transform (HHT) is proposed here to analyze the physical measurements in time domain. It is based on the empirical mode decomposition (EMD), which generate a set of intrinsic mode functions (IMF). The HHT is applicable to non-stationary and nonlinear data analysis, and finding out the instantaneous characteristics including frequency of the data is its main part. Besides, combining Fast Fourier Transform (FFT) with EMD shows the different results with HHT. In the phugoid analysis, we present the comparison between the non-stationary signal analysis, HHT, and the conventional Fourier based method from the real-time flight test data measured by kinematic GPS.

In the second part of this thesis, an application of adaptive all-pass based notch filter (ANFA) with Gaussian-Newton adaptive algorithm in a GPS narrowband anti-jamming system was presented. In the simulations, there are several stationary and non-stationary interferences considered. The ANFA can estimate the instantaneous frequency of the jamming in real-time, and it achieves a better performance than the conventional time-domain adaptive predictors in terms of mean squared prediction error (MSPE) and signal-to-noise ratio (SNR) improvement.

並列關鍵字

instantaneous frequency ； Hilbert-Huang Transform ； empirical mode decomposition ； intrinsic mode functions ； phugoid ； global position system ； adaptive all-pass based notch filter ； Gaussian-Newton algorithm ； narrowband anti-jamming

參考文獻

[1] N. E. Huang, Z. Shen, S. R. Long, et al., “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis,” Proc. Royal Society, pp. 903-995, London, 1998.

[5] H. M. Peng, P. C. Chang, and F. R. Chang, “Hilbert Spectrum for Time Domain Measurement Data and Its Application,” 34th Annual Precise Time and Time Interval Systems and Applications Meeting, pp. 501-510, Reston, Virginia, U.S.A., Dec. 2002.

[6] C. Cai, W. Liu, J. S. Fu, and Y. Lu, “Doppler Frequency Extraction of Foliage Penetration Radar Based on the Hilbert-Haung Transform Technology,” Proc. 2004 IEEE Radar Conference, pp. 170-174, Philadelphia, PA, U.S.A., Apr. 2004.

[8] W. Tang, G. Howell, and Y.-H. Tsai, “Short-Term Accuracy Analysis of Barometric Altimeter,” 11th Saint Petersburg International Conference on Integrated Navigation Systems, pp. 75-77, Saint Petersburg, Russia, May 2004.

[11] A. Nehorai, “A Minimal Parameter Adaptive Notch Filter with Constrained Poles and Zeros,” IEEE Transaction on Acoustics, Speech and Signal Processing, vol. 33, No. 4, pp. 983-996, Aug. 1985.