06-功率谱密度和白噪声过程推荐课件

1、2021/8/2212021/8/222平稳随机过程的功率谱密度平稳随机过程的功率谱密度 白噪声随机过程白噪声随机过程主讲人：张有光主讲人：张有光电电 话：话：82314978办公室：新主楼办公室：新主楼F8062021/8/2232021/8/2242021/8/2252( )Ws t dt 2021/8/226| ( )|s tdt ( )( )j tFs t edt2( )| ( )|Wst dts tdt ？2021/8/2272( ) |( )|EF能量守恒！能量守恒！221( )|( )|2s t dtFd2021/8/22821lim( )2TsTTPs t dtT 2021/8

2、/229( )| |( )0Ts ttTsttT2021/8/2210( , )( )( )Tj tj tTTFTst edts t edt2( )TsTPst dt2021/8/2211221( )|( ,) |2Tst dtFTd2211( )|( , )|24TTs t dtFTdTT2021/8/2212221lim( )211lim|( , )|22TsTTTPs t dtTFTdT2021/8/221321lim|(,) |2TSFTT 2021/8/221422(,)( )11( )|(,) |24TjtXTTXTFTXt edtXt dtFTdTT21lim( )2TXTTPE

3、Xt dtT2021/8/22152221lim( )21lim( )2TXTTTTTEXt d tTEXtd tT 211lim|( , )| 22XXTPE FTdT2021/8/221621( )lim|( , )|2XXTSEFTT1( )2XXPSd2021/8/2217( )XS2( )0( )00XXSG2021/8/22182021/8/2219( )( )jSRed*()( )RR( )S2021/8/22201( )( )2jRSed2021/8/22211212121122()1212()12121( )lim( )( )21lim( )( )21lim()2TTj tj

4、 tXTTTTTjttTTTTTjttTTTSEX t edtX t edtTE X t X tedt dtTR tt edt dtT 2021/8/2222222222| |( )lim() ( )12| |lim( )lim( )2TjXTTTTjjTTTTSRedTRedRedT2021/8/2223|( )|Rd ()( )jXSRed2021/8/222421( )()20,1(0)()|( ) | 02jRSedRSdEX t令则2021/8/2225( )( ), ( )()SSSS*()*()( )( )()( )( )( )( )()jjjjSRedRedSSRedRedS

5、2021/8/222600()2( )cos()1( )()cos()SRdRSd2021/8/2227 coscX tt 0 2, 12()c o scR 12142()()()( )cos()()ccjjcjjccSRededeed 2021/8/2228| |( )Re 22022| | |( )( )cosjjSRedeeded 2021/8/22292424109(),( )SR 求求242142109( )jRed 3195482j|z22| | |1z +4R()=2jez=j,3j2(z +1)(z +9)()ee 在在2021/8/22302211(),( )()SR 求求2

6、1112112214| | | | |()( )()( )( )( )()YYzzXYYSReRRReedzee 已已 知知的的2021/8/22312021/8/22321( )lim( , )( , )2XYXYTSE FT FTT2021/8/2233( )( )jXYXYSRed1( )( )2jXYXYRSed2021/8/223401(0)( )( ) ( )2XYXYRSdE X t Y t2021/8/2235( )0,( )0XYXYRS( )( )( )( )( )( )X YXYX YXYRRRSSS2021/8/2236*( )( )()XYYXYXSSS2|( )|(

7、 )( )XYXYSSSRe()Re( )Im()Im( )XYXYXYXYSSSS 2021/8/2237*1( )( )()XYYXYXSSS）*( )()( )( )() ( ,; , )YXYXYXRRRy t x tf x ty t dxdy先证明：先证明：令：令：tt *( )( ) () ( , ; ,)()YXXYRx t y tf x t y tdxdyR*( )( ),-( )()( )( )jYXYXjjYXXYXYXYSRedSRedRedS令：2021/8/2238*()( )( )( )( )( )()jYXYXjYXYXX tY tSRedRedS 若和是实随机过

8、程则互谱密度函数不是实的、正的偶函数互谱密度函数不是实的、正的偶函数2021/8/22392)|( )|( )( )XYXYSSS1( )lim( ,)( ,)2XYXYTSE FT FTT22221|( ) |lim( ,)( ,)211lim|( ,) | lim|( ,) | 22( )( )XYXYTXYTTXYSE FT FTTEFTEFTTTSS2021/8/22403)Re()Re( )Im()Im( )XYXYXYXYSSSS ( )( )( )cos( )sinRe( )Im( )jXYXYXYXYXYXYSRedRdjRdSjS 2021/8/22412021/8/22420( )(,)2NS ( ),0W t t 相当于相当于信号与系统信号与系统中的冲击响应函数中的冲击响应函数2021/8/22430001( )2212( )( )222jNRedNN 2021/8/2244( )R( )S000S2021/8/2245 10( )00(0)(0)RRRrRRR2