基于過零點-極點估計的瞬時頻率幅度算法
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?zāi)B(tài)分解(EMD)提取信號的內(nèi)蘊模態(tài)函數(shù)(IMF),并對IMF利用Hilbert變換得到信號的時頻幅度譜和邊際譜。在總結(jié)Hilbert變換理論和算法實現(xiàn)局限性的基礎(chǔ)上,提出基于過零點-極點估計求取IMF瞬時頻率、幅度算法,通過對離散信號插值運算精確求取過零點和極點位置,并據(jù)此求出相應(yīng)點的瞬時頻率和幅度,最后采用三次樣條求取信號的瞬時頻率幅度曲線。通過幾個典型的例子對該算法進行檢驗,結(jié)果表明,與Hilbert變換結(jié)果比較,借助該算法得到信號的時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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