基于過零點(diǎn)-極點(diǎn)估計(jì)的瞬時(shí)頻率幅度算法
The Algorithm Based on Zero-Crossing and Extremum Estimation to Obtain Instantaneous Frequency and Instantaneous Amplitude
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摘要: Hilbert-Huang變換(HHT)理論通過經(jīng)驗(yàn)?zāi)B(tài)分解(EMD)提取信號(hào)的內(nèi)蘊(yùn)模態(tài)函數(shù)(IMF)，并對(duì)IMF利用Hilbert變換得到信號(hào)的時(shí)頻幅度譜和邊際譜。在總結(jié)Hilbert變換理論和算法實(shí)現(xiàn)局限性的基礎(chǔ)上，提出基于過零點(diǎn)-極點(diǎn)估計(jì)求取IMF瞬時(shí)頻率、幅度算法，通過對(duì)離散信號(hào)插值運(yùn)算精確求取過零點(diǎn)和極點(diǎn)位置，并據(jù)此求出相應(yīng)點(diǎn)的瞬時(shí)頻率和幅度，最后采用三次樣條求取信號(hào)的瞬時(shí)頻率幅度曲線。通過幾個(gè)典型的例子對(duì)該算法進(jìn)行檢驗(yàn)，結(jié)果表明，與Hilbert變換結(jié)果比較，借助該算法得到信號(hào)的時(shí)頻幅度譜和邊際譜結(jié)果更精確、頻率分辨率更好。Abstract: According to Hilbert-Huang Transform (HHT) theory, the signals Intrinsic Mode Function (IMF) is extracted by Empirical Mode Decomposition (EMD). Its time-frequency-amplitude spectrum and marginal spectrum are obtained by Hilbert transform. In the basis of summarizing the limitation of the Hilbert transform theory and its realization, an algorithm based on zero-crossing and extremum estimation to obtain instantaneous frequency and instantaneous amplitude is presented. The positions of zero-crossings and extrema are obtained accurately by interpolating the discrete signal. The instantaneous frequency and instantaneous amplitude of relative points are obtained. The signals instantaneous frequency and instantaneous amplitude waveform are obtained by cubic spline interpolation computation. By testing the result and comparing the detail of result with Hilbert transform method through several representative examples, it shows that the instantaneous frequency and instantaneous amplitude obtained by zero-crossing and extremum estimation algorithm are more precise and the frequency resolution is better.
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Huang N E, Shen Z, Long S R, et al.. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. of the Royal Society of London, Series A, 1998, 454:903996. .[2]Huang N E, Shen Z, Long S R. A new view of nonlinear water waves: The Hilbert spectrum[J].Annual Review of Fluid Mechanics.1999, 31:417-[3]劉紅星, 陳濤, 屈梁生等. 能量算子解調(diào)方法及其在機(jī)械信號(hào)解調(diào)中的應(yīng)用. 機(jī)械工程學(xué)報(bào), 1998, 34(5): 8590. .[4]李紅. 數(shù)值分析. 武漢：華中科技大學(xué)出版社,2003:17.23. -
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