應用希爾伯特－黃轉換之訊號濾波研究

Signal Filtering Using the Hilbert-Huang Transform

陳振雄(Jenn-Shyong Chen)

《科學與工程技術期刊》 6卷1期 (2010/03) Pp. 75-84

https://doi.org/10.7117/JSET.201003.0075

摘要

本研究嘗試利用希爾伯特－黃轉換(Hilbert-Huang transform, HHT)來進行時間域之訊號濾波。HHT是訊號時頻分析中最先進的技術，可應用於非線性和非穩態的時間訊號。不同於傅立葉轉換(Fourier transform)和基波轉換(wavelet transform)，HHT無須預設任何基底函數，而是利用其獨特的分解方式（empirical mode decomposition, EMD 或ensemble EMD, EEMD）將訊號分解成幾個本質分量(intrinsic mode functions, IMF)，再由IMF之希爾伯特轉換後之複數型式計算出各個IMF之瞬時頻率，藉以呈現訊號頻率隨時間之細微變化。由於可在時間域取得訊號之瞬時頻率，若對各個IMF篩選出濾波頻帶內之時段，再組合篩選後之各段IMF，則可得出濾波後之訊號。本研究首先利用數種模擬訊號進行濾波之分析，結果顯示對於無雜訊之訊號而言，使用EMD方式之濾波效果良好；但是，當訊號受到白色雜訊污染時，則必須利用EEMD來改進濾波效果，其過程也比較費時。最後，本研究針對一段語音訊號進行濾波分析，結果顯示利用HHT來萃取一頻帶內之語音波形確實有一定的效果，不過在較高頻帶處其濾出之波形比較不完美。有鑑於此，目前的EEMD比較適用於後端之訊號分析，對於即時的訊號處理和濾波則仍需進一步探討。

關鍵字

希爾伯特－黃轉換 ； 本質分量 ； 瞬時頻率 ； 雜訊 ； 語音

並列摘要

In this study an attempt was made to employ the Hilbert-Huang transform (HHT) to filter signals in the time domain. HHT is an advanced technique for time-frequency analysis of signals, applicable to both non-linear and non-stationary temporal signals. Differing from the Fourier and wavelet transforms, HHT does not need preset basic functions; instead, its unique sifting process (empirical mode decomposition [EMD] or ensemble EMD [EEMD]) is utilized to decompose temporal signals into certain intrinsic mode functions (IMFs). Through the HHT of each IMF component, the instantaneous frequency at any moment can be estimated, a procedure that can show finer temporal variations in the frequencies of the signals. With the instantaneous frequencies of IMFs, the segments within the frequency band can be extracted on request; moreover, a combination of these IMF segments can indicate the signal after filtering. Several kinds of artificial signals were employed in this study to examine the aforementioned filtering process. For signals without noise, the consequence of using EMD is excellent; whereas, for noise-contaminated signals, a more time-consuming EEMD is needed to improve the filtering. Finally, the filtering of an audio signal was also attempted. The results demonstrate that, to a certain extent, signal filtering via HHT is feasible although the resultant wave shape in the higher frequency bands is less complete. According to these investigations, the present EEMD is more suitable for post-analysis. However, further study is needed for on-line signal processing and filtering with EEMD.

並列關鍵字

Hilbert-Huang transform ； intrinsic mode function ； instantaneous frequency ； noise ； audio signal