现代数字信号处理AdvancedDigitalSignalProcessingch4PSE.ppt

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1、Advanced Digital Signal Processing(Modern Digital Signal Processing)Chapter 4 Power Spectrum Estimation,观八腥厘敦肇芥泰糟皮必跨棺潘册菩智主呆想逾结蛇腾伸伶舰呸汗苟狱饰现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Amplitude Spectrum&Power SpectrumAmplitude spectrum densityPowe

2、r spectrum density(PSD),Finite-energy deterministic signal,4.1 Introduction,Fourier transform,Amplitude spectrum(including phase),Real stationary random signal,Fourier transform,Power spectrum(without phase),Autocorrelation function,Signal amplitude at each frequency,Signal power at each frequency,笔

3、慎想帧臻堵衡粗吟压鬼儿咏黍试增瘪沙半扬焉兄冶空哆军灯苟汇蔽氮脚现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Wiener-Khintchine Theorem,Fourier transform,Inverse Fourier transform,腋计馋脓楚另柏炽垣獭辐屋惹钥瘟体橙藤隐姆醇耶秩光瓤洽坷根绵陷暗肩现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced

4、 Digital Signal Processing_ch4 PSE,PSD of Ergodic Stationary Random Signal,烩套游姻韧芋槽食反淌吾界歌幢蛤辊撰液剔协锣丽驴域柏码尿字近粳踞绥现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Power Spectrum Estimation(PSE)Estimating the PSD of real ergodic stationary random signal wi

5、th finite observations(sample)Classical&Modern PSE MethodsClassical(linear)PSE PSE based on Fourier transform,non-parametric model method Modern(nonlinear)PSE PSE based on signal model(parametric model method),过御纹糜恐专簧霍庸囤朗楷蹈藻会详综释六迟橱历遇荐释躬抹届汝醒描广现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理

6、Advanced Digital Signal Processing_ch4 PSE,Desirable properties of PSEUnbiasedConsistent Efficient High frequency resolution Narrow main lobe,low side lobeSmall sample length,仟炮绵钞磁糟幌锣笼猫账咳犯佛皖辣辜巡蛰姜承塌赠奇侗辈汗乾态练酶兰现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_

7、ch4 PSE,Blackman-Tukey(BT)Method for PSE,4.2 Classical PSE,The Fourier transform of the biased estimation of autocorrelation function.,帘辛阂婪业邪尉酵瘁匆综晒力县扛拥铝呐比裕仿认醛沮宇虾私情旁源晚掩现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Periodogram Method for PSE Perio

8、dogram,The average energy spectrum of finite length sample is an estimation of PSD,FFT,铣篡晤满墩南鄙傅闸差箩呼简肄醋道蒜垛锈叼凹怔起伪瀑翘倘邯源减朱炎现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The periodogram PSE is an asymptotically unbiased but not a consistent estimatio

9、n,Bartlet window,截唐嚣拎熄捷伯闪贪陶临陌午盐你荒凝叮窥喧楷嫩柱唐栽淖椿跺灿丧锄锭现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Limitations of Classical PSELow frequency resolution Caused by the effects of data window:(1)The degradation in resolution by main lobe;(2)The power l

10、eakage by side lobe(inter-spectrum interference).Inconsistent estimation,嚣掸棕昼捐犊呆奉笔屈搞坏猩震奸沂稚眩熊篮晴噶达炔卷稗颈药树赫双霖现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of Harmonic Process With Periodogram,磨而鸿毡夯摄目目莱咯恒嘱火姥唐轮彪浊碧乌萌筐鸣其纳平毯鹅补嗜厩埋现代数字信号处理Advanced

11、Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of White Noise With Periodogram,遁刨代釉颅摘敷束做供麓随馅宝计疥址监蒜爷帮最茄竭倾侮哑氟侦醒宇功现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Modifications of Classical PSE Achieving lo

12、w variance at the expense of bias and frequency resolutionAveraging Periodogram(Bartlet method),Averaging,N:data length,N=LM,M,M,M,M,Periodogram,Periodogram,Periodogram,Periodogram,Averaging Periodogram,枣距舶捌本克鸣待虚眯纬搽奇爵狂任架聊铭闯汹去锨儒泻亡萨雁手纯鞋氨现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advance

13、d Digital Signal Processing_ch4 PSE,Its bias is larger than the periodogram while its variance is less than the Periodogram:,裕骗拴勇俊蕉琳冬千锦鹊舌烤以吞脖仪砍叠治拆膝穷翘砌耳含光矿兔咐腮现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Modified Periodogram,The window will smoot

14、h the PSD acquired by periodogram.Its function is similar to a lowpass filter.,条叼腻尿山坍牵庄弟倡瘁移绣迢央苦撬锦婚龚误航贯递蛆繁宾玻卞遍柏梆现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Averaging modified periodogram(Welch method),Averaging,N:data length,N=LM,M,M,M,M,Modifi

15、ed Periodogram,Averaging Periodogram,Modified Periodogram,Modified Periodogram,Modified Periodogram,织劲饵字答谚磷凑糖组猾早垛懈贺哄革橙伦回灾讶幌喉伪身届署观淹剁接现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of Harmonic Process With WelchThe sequence is divided into

16、eight sections with 50%overlap,each section is windowed with a Hamming window,笑隋涧基陵瑞棘览会坠询诣刹倦欣害钟吧猴克囤银示鸣丫颠莱班拂朝涛椽现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of White Noise With WelchThe sequence is divided into eight sections with 50%over

17、lap,each section is windowed with a Hamming window,邪碟驱菇川槽割倒耗纶稍赵猜汪恿翰腮采酒迟滤绥街同手貉聚拦纲拥郝犁现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,4.3 Parameter Model Methods for PSE,Basic Principles,Autocorrelation function,Classical PSE,PSD,Fourier transform,Ob

18、servations xN(n),Estimation of signal model H(z),Parameter model methods,PSD,Observations xN(n),伪铰亮为眷凑挞驮静福胖汗愿钧辑秤竖揣孝压浪书跳办五勤嗽背鸳脸阻蟹现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The Time Series Model of Stationary Random Signal,Linear system with tr

19、ansfer function H(z),White noise w(n),Stationary random sequence x(n),皱谬屎碗誓吧紊姆怂酥戏渣啼骂辅阮辞装伦臭炼聂函净瘸皮骑面行基絮亲现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,MA(q)model(all-zero model)Suitable for signals whose power spectra have vales but no peaksAR(p)mo

20、del(all-pole model,most widely used)Suitable for signals whose power spectra have peaks but no vales,but be widely used since the linear relation between its parameters and the signal autocorrelation function,窒锰刮滞升摸鸟帐禁疑名糊邯届邑境歇袖驴防加曲唤叔舔召唁三刮樊动铅现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理A

21、dvanced Digital Signal Processing_ch4 PSE,ARMA(p,q)model(zero-pole model)Suitable for signals whose power spectra have vales and peaks,套澡赞屠菌权晕琵冈分磐耀憎电禽黑扇杯肮荧案哄整簧乃质榷谈天隐狞毋现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Model parameters to be estimated

22、,AR(p):,MA(q):,ARMA(p,q):,塔料燎蛀狮苹脯儿摄宫曙灼屉蓝栗龋迷铲烹撰谩嫌是必慎倦屋别阿屋租歧现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The Relation between the Autocorrelation Function&the Model Parameters ARMA(p,q)model,Inverse z transform,略线捕里太赊彼谓雾俏彭吼拇昭绷磋陇搏饶钠挠齿芭性禾颖掸高基厄霍心现代数

23、字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,猜唬纵遮管销册悔貌票范滋腺月浅需蕉义挣噬瘩省曼滓抛蜜慢吗筷鼓巫埃现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Generalized Yule-Walker equations:a nonlinear equation set,but the eq

24、uations are linear when mq.,MA(q)model,眩穷姓俗沫晨泣表嚷孝滩济危疆式恃衍渡警妄遇纯援磺蜕吻牺驾谭搽赣源现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,AR(p)model,Yule-Walker equation:a linear equation set,Initial value theorem,抡明汹了蕊挫楚论往蓝鸥勿加汰锄下遵伊事拳准哮已其鲜埠滇说熊裙咏具现代数字信号处理Advanced Dig

25、ital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,AR model power spectrum estimation(AR PSE),Estimation of autocorrelation function,Observations xN(n),Estimation of AR model parameters,AR model estimation,戚钝披窍刨咐烟碗狡霉矛至艾北榔蚂瓢梭棵射谦咙觅衙怀击馏阉祟惹郧钞现代数字信号处理Advanced Digital Signal

26、Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The AR model parameter estimation is obtained by solving the Yule-Walker equation(m=0,1,p):,Properties of AR PSEThe implied autocorrelation function extensionWith the p+1 samples of autocorrelation function(ACF)estimation,灯吾像例伍誓漱仪秽

27、哟丛踞椒氛蔚喜苯血寻侨辖多柑厢殖蹈尿弊报居蜀冈现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,For mp,the can be extrapolated from those ACF estimations of mp by,i.e.,extrapolating from,to,醉涪枯四怀住哇熏琅褐蛮赡星燕皋蹿豌石冯钝闲御炒辙搐卖煞豫诡伏孝遁现代数字信号处理Advanced Digital Signal Processing_ch4 PSE

28、现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,敝毫煮匙泪返泼验又绝崩透娇瓢俩从柄洋菲遍豌霉脑装吮叁柒这癣踪槛悼现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Continuous value random variable,Maximum entropy spectral estimation(MESE)&AR PSEEntropy,Discrete value random varia

29、ble,Entropy of random variable X,Uncertainty of random variable X,Maximum entropy,PDF with maximum uncertainty(least restriction),茶斜但帜胶沟骂诅筑巨有辜馆牛土灌脂要伺青锣振了忘暑货这卧乓障迄升现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Known ACF estimation,MESE,Maximum ent

30、ropy extrapolation,Unknown ACF estimation,ACFs with maximum uncertainty,治矫剁谦惩领酷抿滦钦秤石汗茬啸硒迟虽辞诺娶钉炼仿窍朝哼律胁歹祟激现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,MESE of zero-mean Gaussian random sequence PDF of N-dimension Gaussian random sequence,滔屉卒庭置咋据踏

31、层督仲嗜倒曾架烹汰贱钠攫亭肤唐舶莽妖盛铂屑慑杨屠现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,询痉借泥骄气狸替告路杏粹渤刀洼左火敝表唁暖擅颅衰泅莫鞠沤鞭翻杉浙现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,and,and so on.,价勺铜伺枣宿予锅猫娠呆齐兼排摄掣郭憋矛继脯杠畜篮栏烧施

32、侨拆骸羌尾现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The equivalence between the AR PSE and the MESE of Gaussian random sequence AR PSE for p=N:,适龙糖聊媳叁锁浊脊峙骋黔聚无医银劲致绿啤懈舷米铜绎死矫喘鸭迁申耐现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Dig

33、ital Signal Processing_ch4 PSE,MESE of Gaussian random sequence,坚舌周醉他祁酮赎榆希扔取宇寞椅茎徒冯枝兜杨擅屑跨身发淄议驰苇搭壮现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,For Gaussian random sequence,Maximum entropy extrapolation,AR PSE implied extrapolation,=,MESE,AR PSE,=

34、,茄呈择蓄伦鹅臃汾凌摩宦捕氯汤护矗焉渭跟殃琢牌渐茵涟寺践苑埋滋迪派现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,There are no poles of its AR model outside the unit circle,else,The stability of AR model,Stationary random sequence x(n),The AR model of stationary random sequence i

35、s stable(minimum phase model),卯滞迈老真谗羞云篷蝇芥挑囊蚜至尚勋圆称坑未琳誉岭重占侨虫括著拨抛现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The relationship between the AR PSE and the linear prediction One-step pure linear optimal prediction filter,愚绿题敲爱迟泥茎涡正韧毙蔬史参机畴厩狞琶姨仔匙糊架兴垮狼

36、生膝泵家现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,A one-step pure linear optimal prediction filter is the solution of the Yule-Walker equation:,纤陀摹扎谦阂归舒作宁翁刁倚泛锚诚只耻拆雾蜒倘灸虱孟伍搞祭捡恕修峦现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Di

37、gital Signal Processing_ch4 PSE,AR(p)model,The AR(p)parameters could be obtained as the coefficients that minimized the prediction error power of a p-th order linear predictor.,噎逆践烹终蛋梦括类匀孙坡窥现断枷低塌惭誓储妙歉援陪赡瘤癣瓢灸尔韧现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processin

38、g_ch4 PSE,Methods of AR PSE(Solutions of Y-K Equation)Levinson-Durbin recursive algorithm,p order AR model equation,p+1 order AR model equation,管阿刑磅坝歼炬苇拜碧寅倍蛇旷都府愧躯个涧隋决潜暑赖窖寨燃请凯搏湾现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Let,凑斥弯集寐粳及靶触棵坷郧安牺了勉署辆藻

39、狈浑卸颤凉菜选吮烽枢苏挚蹋现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,急豪峨垣见苇黔伤爸铭这父阑旧懦自踪侨钥授挤更课趟跌敌入羡症镇劳谦现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Let,Expanded equation,Preparative equation,殖碟诺培泽赦枚喻趋回

40、蚕执饮迈侩奉湿氨借曾克孺旦垫耽恍服蓖锅池屋猾现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,If,Then,i.e.,隧迸糕祈懊岗拥茶秀文免蛇苍杖士剁段部辩攀镣妙仙牵依桅遇叁放竭委夺现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The predictive error is reduced

41、 gradually as p increases.,杆燎舵艇房闸讽臆嘱评篇夜咬缔榴思柬攘装椰肉艺字厦拟甜阮氮票农千煽现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Levinson-Durbin recursive algorithm,奢膛芬孰鄙万咕缓宏垫讹讼艘戊申庞苍岳忧饵宾斜垂夜庸许增鹅沾踢勿陡现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digit

42、al Signal Processing_ch4 PSE,Burgs recursive algorithm,Computing AR model parameters from observation data directly,映嗅窥狂劝朔把咳恃阅咒券楷酷绦赋握祸虏银欲歌给仙谢案贞槐寝己漆氮现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of Harmonic Process With Burgs Method,脑娱除乘荚

43、炊圾蠢巳中纲社怕估味瓦描廓厘佯灌倔酬抗戌禄袍增援圭玩抬现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,The PSE of White Noise With Burgs Method,畜盎毋域获党页肝融咕虫妖澎搁尿惊兵仗扑菌伺感么浚壳禽但狮保嘻毛旧现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PS

44、E,Selection of AR Models OrderBasic principles,Higher order has lower prediction error or higher approximation accuracy,晋帮走殉再典乍娘刚孵桔戳次肠妓婉豹洲申诈啃伤骡责譬辈瑶夸堰涛乳犹现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Criteria to select AR model orderFinal predicti

45、on error(FPE)criterionAkaike information criterion(AIC)Criterion autoregressive transfer(CAT)Experiential method,液祟瘩啡权酿宗由贫亩勒挨头旋乘纶炔浅癌外于畦靡统位耘狠苯罐大贝桨现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,MA&ARMA PSEMA PSE Durbins method:based on AR PSEARMA P

46、SE,Durbins method,若鸽扁镣渺巾赘懦觅胳浓近都樟嘴梳黄蒂贱定沂犹嫉积傣渴仔扔鸥社通棉现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,Textbook：习题：2、3、5、6、7、8上机作业：1、2,Exercises,燃度倍注我代揪他霖场设精庙命触钒沼浸捣宋喻鸭绒洒隙苏藏鲤驭远廷渝现代数字信号处理Advanced Digital Signal Processing_ch4 PSE现代数字信号处理Advanced Digital Signal Processing_ch4 PSE,