1、MEASUREMENTINFORMATION SIGNAL ANALYSIS IN MECHANICAL ENGINEERING 機(jī)械電子信息工程系 杜潤生 李錫文 匿名登陸 機(jī)械工程測試信息信號分析 Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20221Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011

2、Aspose Pty Ltd.8/27/202222 周期信號的頻譜分析 周期信號是經(jīng)過一定時(shí)間可以重復(fù)出現(xiàn)的信號，滿足條件： x ( t ) = x ( t + nT ) 任何周期函數(shù)，都可以展開成正交函數(shù)線性組合的無窮級數(shù)，如三角函數(shù)集的傅里葉級數(shù):Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20223展開成三角函數(shù)的無窮級數(shù)形式設(shè)周期函數(shù)f(t)的周期為T周期信號三角形式的FS信號的基波、基頻系數(shù)an和bn統(tǒng)稱為三角形式

3、的傅里葉級數(shù)系數(shù)，簡稱為傅里葉系數(shù)(FS)。相位譜幅值譜功率譜Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20224系數(shù)計(jì)算方法設(shè)周期函數(shù)x(t)的周期為T，展開成復(fù)指數(shù)函數(shù)的無窮級數(shù)形式：周期信號復(fù)指數(shù)形式的FS平均功率相位譜幅值譜功率譜Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose P

4、ty Ltd.8/27/20225FS0t-0時(shí)域信號頻域信號連續(xù)的周期的非周期的離散的正：反：Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20226周期信號傅里葉頻譜特點(diǎn)周期信號的傅里葉頻譜特點(diǎn)：諧波性：僅在一些離散頻率點(diǎn)(nf1)上有值，各次諧波頻率比為有理數(shù)。離散性：各次諧波在頻率軸上取離散值，離散間隔為：收斂性：各次諧波分量隨頻率增加而衰減。Cn是雙邊譜，正負(fù)頻率的頻譜幅度相加才是實(shí)際幅度。信號的功率為帕斯瓦爾方程Ev

5、aluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20227周期信號的頻譜譜線的間隔為非周期信號可以看成是周期T趨于無限大的周期信號非周期信號的譜線間隔趨于無限小，變成了連續(xù)頻譜；譜線的長度趨于零。周期信號的頻譜譜線的長度為解決方法FT變換非周期信號-傅里葉變換Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 As

6、pose Pty Ltd.8/27/20228非周期信號的傅里葉變換FT：IFT：變換核FT/IFT的性質(zhì)唯一性：如果兩個(gè)函數(shù)的FT或IFT相等，則這兩個(gè)函數(shù)必然相等?？赡嫘裕喝绻?，則必有 ，反之亦然。FT存在的充分條件：時(shí)域信號絕對可積。非周期信號FTEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/20229FT00t時(shí)域信號頻域信號連續(xù)的非周期的非周期的連續(xù)的對稱性：時(shí)域連續(xù)，則頻域非周期。反之亦然。Evaluation o

7、nly.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/202210信號的傅里葉變換一般為復(fù)值函數(shù)，可寫成幅度頻譜密度函數(shù)相位頻譜密度函數(shù)FS與FT比較Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/202211FT的性質(zhì)線性性：齊次性和疊加性反褶和共扼性：奇偶虛實(shí)性：實(shí)信號和虛信號的FT幅度譜函數(shù)

8、是偶函數(shù)，幅度譜偶對稱。對稱性(對偶性)：FT與IFT的變換核函數(shù)是共軛對稱的。尺度變換特性：時(shí)域壓縮對應(yīng)頻域擴(kuò)展，時(shí)域擴(kuò)展對應(yīng)頻域壓縮時(shí)移特性：與尺度變換結(jié)合頻移特性：與尺度變換結(jié)合。時(shí)域信號乘上一個(gè)復(fù)指數(shù)信號后，頻譜被搬移到復(fù)指數(shù)信號的頻率處。微分特性，積分特性；卷積定理，時(shí)域相關(guān)性定理，帕斯瓦爾定理。Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/202212信號理想抽樣前后頻譜的變化原始信號及其頻譜沖激序列及其頻譜抽樣信號

9、及其頻譜抽樣間隔發(fā)生變化時(shí)域離散頻域周期抽樣信號的FTEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/202213按間隔Ts進(jìn)行沖激串抽樣后信號的傅里葉變換，是周期函數(shù)，是原函數(shù)傅里葉變換的Ts分之一按周期2/Ts所進(jìn)行的周期延拓。結(jié)論1：時(shí)域離散頻域周期結(jié)論2：抽樣信號的FTEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2

10、004-2011 Aspose Pty Ltd.8/27/202214傅里葉變換形式的歸納時(shí)間函數(shù)頻率函數(shù)連續(xù)和非周期非周期和連續(xù)連續(xù)和周期(T0)非周期和離散(0 =2/T0)離散(T)和非周期周期(s=2/T)和連續(xù)離散(T)和周期(T0)周期(s =2/T)和離散(0 =2/T0)Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Pro.Copyright 2004-2011 Aspose Pty Ltd.8/27/202215隨機(jī)信號的功率譜密度隨機(jī)信號：時(shí)域無限、不可積分；其頻率、幅值、相位都是隨機(jī)的，不能直接FT; 統(tǒng)計(jì)特性的功率譜密度作譜