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研究生：	李尚胤 Lee, Shang-Yin
論文名稱：	脈聲儀定性校正與時頻轉換之應用 Qualitative Identification of Sonocardiography System and Applications of Fourier Sine Spectrum and Spectrogram
指導教授：	鄭育能 Jeng, Yih-Nen
學位類別：	碩士 Master
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2008
畢業學年度：	96
語文別：	中文
論文頁數：	102
中文關鍵詞：	傅立葉正弦時頻圖、傅立葉正弦頻譜、頻率響應
外文關鍵詞：	Fourier sine spectrum, frequency response, Fourier sine spectrogram
相關次數：	點閱：95 下載：8
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本文對尤芳忞教授所發展的脈聲儀系統之麥克風作定性校正，以證
明在0.5-10Hz 之間，可以產生有效的頻率響應。實驗所用的部份包括訊號產生器、小型揚聲器、小型麥克風、音效卡和個人電腦等。電腦收集到訊號後，應用傅立葉正弦頻譜和傅立葉正弦時頻圖產生器以檢視其頻率響應。該產生器包括下列過程：使用疊代式高斯平滑法移除非週期和極低頻部份，再用單調式三次方分段內插法，定出週期性部份數據靠近兩端的零點，經內插重新分佈點及奇函數轉換，以快速傅立葉級數轉換法，求取傅立葉正弦頻譜。隨後對頻譜取有限的帶狀頻帶後，對其做快速逆傅立葉轉換，求得傅立葉正弦時頻之實數部份，再應用希爾伯特轉換求振幅並畫出時頻圖。從實驗結果得知，只要在足夠小的空間裡，揚聲器有足夠能量推動其發聲膜片，以產生壓力波，麥克風就可以量測到低頻訊號。因而證明脈聲儀系統可以量得到人體手腕的脈博訊號。本文並配合王唯工博士等人所發展的人體動脈之壓力波共振理論，討論動脈訊號，以分析在剖腹產手術過程量取到的ABP 和ECG 訊號。時頻圖可以顯示代表身體各器官之諧波，隨著時間產生的振盪與變化，也可觀測出手術中各個不同的施行點。

The frequency response of the microphone of the Prof. F. M. Yu’s sonocardiography system is qualitatively proven to cover the 0.5 to 10 Hz zone. Experimental equipments include a function generator, small speaker,small microphone, audio board, and personal computer etc.. After the computer receives a signal from the microphone, we apply the Fourier sine spectrum/spectrogram generator to show the frequency response. The transformation involves the following steps. The non-sinusoidal part and extremely low-frequency part are removed by applying the iterative Gaussian smoothing method. In the remaining sinusoidal part, zero points around the two ends are identified by a searching procedure and interpolation. After dropping segments beyond the two zero ends, the corresponding Fourier sine spectrum is obtained by performing an odd function mapping. The time-frequency transform then imposes finite bandwidth Gaussian window upon the Fourier sine spectrum centered at a given frequency. The inverse Fourier transform of the band-pass limited spectrum gives the real part of the resulting spectrogram. The experimental results show that, in a small space, as long as the speaker has enough energy to push that small air cell, the microphone will receive low-frequency signal. According to the Wang’s frequency resonance theory of arterial and vascular system .We apply it to invest the pulse signal of a caesarean section including ABP and ECG signals.The corresponding spectrums and spectrograms show that every corresponding harmonic mode has amplitude and frequency variations with respect to time. We also compare the different operation point to explain its meaning with the spectrograms.

目錄
摘要 ............................................................................................................. I
Abstract ..................................................................................................... II
誌謝 .......................................................................................................... IV
目錄 .......................................................................................................... VI
圖目錄 ...................................................................................................... IX
符號說明 ................................................................................................. XII
第一章 序論 .............................................................................................. 1
1.1 研究動機.......................................................................................... 2
1.2 研究目的........................................................................................... 3
1.3 文獻回顧........................................................................................... 4
第二章 實驗設備與實驗步驟 .................................................................. 8
2.1 實驗設備........................................................................................... 8
2.2 實驗步驟........................................................................................... 9
2.2.1 小型麥克風(脈搏感測器)頻率響應之定性校正 ................... 9
2.2.2 侵入式手腕血壓訊號量測 .................................................... 10
2.2.3 心電圖訊號 ........................................................................... 11
第三章 理論分析 .................................................................................. 14
3.1 電容式麥克風基本構造與錄音原理 ............................................ 14
3.2 共振理論........................................................................................ 15
3.3 修正型單調性三次方分段內插法 ............................................... 16
3.4 疊代式濾波器法 ........................................................................... 17
3.5 低誤差傅立葉正弦頻譜法 ........................................................... 23
3.6 小波法-Morlet 轉換式 ................................................................... 25
3.7 強化的Morlet 轉換式................................................................... 28
3.8 希爾伯特(Hilbert)轉換式 ............................................................. 28
3.9 Gabor 轉換式 ................................................................................. 29
3.10 新時頻圖(spectrogram)產生器 ................................................... 30
第4 章 結果與討論 ................................................................................ 34
4.1 電容式麥克風的頻率響應校正 ................................................... 34
4.1.1 揚聲器1(口徑21.85mm)之不同漏氣量的頻率響應 .......... 35
4.1.2 揚聲器2(口徑10mm)之不同漏氣量的頻率響應 ............... 36
4.1.3 揚聲器1 和2 的比較 ............................................................ 37
4.1.4 揚聲器1 和2 的頻譜圖在不同漏氣量之比較 .................... 38
4.1.5 揚聲器1 在微量漏氣和使用凝膠密封的頻譜圖比較 ........ 38
4.1.6 揚聲器2 在微量漏氣和使用凝膠密封的頻譜圖比較 ........ 39
4.1.7 揚聲器2 在0.5hz 和5hz 之微量漏氣的時頻圖比較 ......... 40
4.1.8 揚聲器2 在0.5hz 和5hz 之少量漏氣的時頻圖比較 ........ 40
4.1.9 微量漏氣之揚聲器1 和2 的頻率響應圖比較 .................... 41
4.1.10 小量漏氣之揚聲器1 和2 的頻率響應圖比較 .................. 41
4.1.11 凝膠密封之揚聲器1 和2 的頻率響應圖比較 .................. 42
4.1.12 揚聲器1 和揚聲器2 的頻率響應圖在不同漏氣量之比較43
4.1.13 麥克風定性校正之結論 ..................................................... 44
4.2 一般剖腹產[32] .............................................................................. 44
4.2.1 第一個剖腹生產訊號分析 .................................................. 45
a.剖腹生產開始十四分鐘訊號 ............................................... 46
b.小孩出生前後訊號 ............................................................... 46
c. 剖腹產手術結束前十分鐘訊號 ......................................... 47
d. 振幅對時間的變化 ............................................................. 47
e. 頻率對時間的變化 ............................................................. 48
4.2.2 第2 個剖腹生產訊號分析 ................................................... 49
a. 剖腹生產開始十四分鐘訊號 ............................................. 49
b. 小孩出生前後訊號 ............................................................. 49
c. 剖腹產手術結束前十分鐘訊號 ......................................... 50
4.2.3 剖腹產手術之結論 ................................................................ 50
第5 章 結論與未來工作 ........................................................................ 51
參考文獻 .................................................................................................. 53
結果附圖 .................................................................................................. 58
圖目錄
圖2.1 脈搏感測器 .................................................................................. 58
圖2.2 波型產生器(Function Generator) ................................................. 58
圖2.3 音效卡 .......................................................................................... 59
圖2.4 利用A-Line 連續量測動脈壓 .................................................... 59
圖2.5 心電圖(ECG)與連續動脈壓波形(ABP)..................................... 60
圖2.6 橫平面電極位置 .......................................................................... 60
圖2.7 胸導極位置 .................................................................................. 61
圖3.1 電容式麥克風基本構造 ............................................................... 61
圖3.2 電容式麥克風傳輸電路簡圖 ....................................................... 62
圖3.3 疊代高斯法過渡區會隨著疊代次數的增加，而縮小其過渡區的寬
度 .............................................................................................................. 62
圖3.4 對第零和第一階(M=0，1)和二次及三次移動式最小平方法(M=2，
3)合適的平滑因子
1 c
λ σ ........................................................................... 63
圖3.5 對第零和第一階(M=0，1)和二次及三次移動式最小平方法(M=2，
3)合適的疊代步驟m .............................................................................. 63
圖3.6 應用疊代高斯平滑法之結果，當原來數據不具週期性特性時，在
數據兩端，會產生斷點 .......................................................................... 64
圖3.7 兩端有誤差，則需要將兩端的數據移除，才能得到好的結果64
圖3.8 低誤差頻譜法與其它頻譜法之誤差比較 .................................. 65
圖3.9 原Morlet 轉換的能量之小波圖 ................................................. 65
圖3.10 強化後的轉換之對應小波圖，在頻率(或尺度函數、波長)之座標
方向的解析大為提升 .............................................................................. 66
圖3.11 最佳的Gabor 轉換式的時頻圖 ............................................... 66
圖3.12 最佳的Gabor 轉換式之3D 圖 ................................................ 67
圖4.1a 驗證脈搏感測器頻率響應之實驗示意圖 ................................ 67
圖4.1b 揚聲器1(口徑21.85mm)的實驗示意圖 .................................. 68
圖4.1c 揚聲器2(口徑10mm)的實驗示意圖 ........................................ 69
圖4.2a 揚聲器1(口徑21.85mm)產生sine 波在量到的頻譜圖-微量漏氣
.................................................................................................................. 70
圖4.2b 用揚聲器1(口徑21.85mm)產生sine 波量到的結果-小量漏氣
............................................................................................................ …..72
圖4.3a 用揚聲器2(口徑10mm)產生sine 波量到的結果-微量漏氣 .. 74
圖4.3b 用揚聲器2(口徑10mm)產生sine 波量到的結果-小量漏氣 .. 76
圖4.4 用揚聲器1(口徑21.85mm)產生sine 波量到的結果-使用凝膠密
封………………………………………………………………………78
圖4.5 用揚聲器2(口徑10mm)產生sine 波量到的結果-使用凝膠密
封………………………………………………………………………80
圖4.6a 揚聲器2(口徑10mm)在微量漏氣情況下0.5hz 的時頻圖 ..... 82
圖4.6b 揚聲器2(口徑10mm)在微量漏氣情況下5hz 的時頻圖 ........ 82
圖4.7a 揚聲器2(口徑10mm)在小量漏氣情況下0.5hz 的時頻圖 ..... 83
圖4.7b 揚聲器2(口徑10mm)在小量漏氣情況下5hz 的時頻圖 ........ 83
圖4.8 揚聲器1(口徑21.85mm)的頻率響應圖-微量漏氣 ................... 84
圖4.9 揚聲器2(口徑10mm)的頻率響應圖-微量漏氣 ........................ 84
圖4.10 揚聲器1(口徑21.85mm)的頻率響應圖-小量漏氣 ................. 85
圖4.11 揚聲器2(口徑10mm)的頻率響應圖-小量漏氣 ...................... 85
圖4.12 揚聲器1(口徑21.85mm)的頻率響應圖-使用凝膠密封 ......... 86
圖4.13 揚聲器2(口徑10mm)的頻率響應圖-使用凝膠密封 .............. 86
圖4.14a 剖腹生產(case1)開始14 分鐘ABP 時頻圖 ............................ 87
圖4.14b 剖腹生產(case1)開始14 分鐘ECG 時頻圖 .......................... 88
圖4.15a 注入升壓藥前5 分鐘到手術開始前之ABP 訊號 ................. 89
圖4.15b 注入升壓藥前5 分鐘到手術開始前之ECG 訊號................ 90
圖4.16a 剖腹生產開始動刀到出生前後之ABP 訊號 ........................ 91
圖4.16b 剖腹生產開始動刀到出生前後之ECG 訊號 ......................... 92
圖4.17a 手術結束前10 分鐘ABP 訊號 .............................................. 93
圖4.17b 手術結束前10 分鐘ECG 訊號 .............................................. 94
圖4.18a ABP 訊號振幅對於時間的變化 .............................................. 95
圖4.18b ECG 訊號振幅對於時間的變化 .............................................. 95
圖4.19a ABP 訊號頻率對於時間的變化 .............................................. 96
圖4.19b ECG 訊號頻率對於時間的變化 .............................................. 96
圖4.20a 剖腹生產(case2)開始14 分鐘ABP 時頻圖 ........................... 97
圖4.20b 剖腹生產(case2)開始14 分鐘ECG 時頻圖 ........................... 98
圖4.21a 剖腹生產開始動刀到出生前後之ABP 訊號 ......................... 99
圖4.21b 剖腹生產開始動刀到出生前後之ECG 訊號 ...................... 100
圖4.22a 手術結束前10 分鐘ABP 訊號 ............................................. 101
圖4.22b 手術結束前10 分鐘ECG 訊號 ............................................. 102
                                    

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