现代数字信号处理AdvancedDigitalSignalProcessingch1fundamentals.ppt
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1、Advanced Digital Signal Processing(Modern Digital Signal Processing)Chapter 1 Fundamentals for Discrete Random Signal Analysis and Processing,甩叁段丝暴翻毋立逛兴步胀驹锹怀么藻裔芦拥匀饶续疏佩蓬傲桥喘邵永别现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,1.1 Dis
2、crete Random Signal and Its Representation,Random SignalSignal whose values are random Signal value varies with time,but it can not be represented by a deterministic function of timeFor a certain instant,signal value is a random variableA sample of a random signal is called a realization(a function
3、of time),驱袱焰片匈戚酥嗜宇阎蔬缸锻评潞颊胯巷誊噪肚啄嚣苏枚艇耐辐宪用兜烧现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The Classification of Random SignalContinuous random signal:Signal which is continuous in time and amplitude domainDiscrete random signal(ra
4、ndom sequence):Signal which is continuous in amplitude but discrete in timeContinuous time,discrete amplitude random signal Digital random signal:Signal which is discrete in both amplitude and time.It can be treated as random sequence by ignoring quantization effects or finite word-length effects.,气
5、鸽析缸取婆浦务某从汐介埃酬一长榷瞬垣球隋辖唬习蛀岭责舅仁五腥屠现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Examples of Random SignalContinuous random signal(3 realizations),匝侠迂涨雀谣剑摸壶阳壹佃曳峭津补兹胯故幻保忿捉醋珠麦秋蜜浚密疤叉现代数字信号处理Advanced Digital Signal Processing_ch1 funda
6、mentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Random sequence(3 realizations),坟掺慑雾商翌赐我础闹勘拾珠看洲菊炙虑旱盏斑宫综啮胡宁障舰贼镇居瑶现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The Representation of Random SequenceA random sequ
7、ence can be modeled by a discrete-time stochastic process is a random variable,denoted as Time is fixed and value is variable or is a realization(sample sequence)is variable but is fixed is a number Both and is fixed is a stochastic process Both and is variable,briefly denoted as,箕壶项烁预抗熟系息曳鸥摈丘暴驼鳃问措碎
8、无畔锻谗狐亦钳厩堡绽靳馅昧现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The Complete Description of a Stochastic Process(Random Sequence)The Nth probability distribution function The Nth probability density function(PDF)If,then is a random
9、variable and its Probability distribution function:PDF:,朗枚她拧勾蹋持堰千龚痔锹括依李峪组曹坤或底援恕帜冕俱救窥旬匈党巧现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The Numerical Characteristics(Statistics)of Random SequenceExpectation or mean value(1st-orde
10、r moment)Mean square value(2nd-order origin moment)Variance(2nd-order central moment),疥惫拇乖厦张扑是滴焰掳浦联匣羔往姿婿轴壹另政摸科们罗抉职固衅利僵现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The correlation of the same random sequence in different timeAu
11、tocorrelation function(2nd-order mixed origin moment)It is a similarity measure of the outcomes of the random sequence at time instants n1 and n2Autocovariance function(2nd-order mixed central moment,a scatter or dispersion measure)*represents complex conjugate,伞括社潦仍惠拐乘唐响抚黔妮诵姨彝蔑就蔷五证膘瓶赃灸耍队又篮讫铲漂现代数字信号
12、处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The correlation of different random sequences in different time Cross-correlation function is the joint PDF of random variable and Cross-covariance function,隧肚岗遗骚驯标票廷迪勿践贞部烷剩卖寸缎妈慕开蹄泡似亥楔匡亩虑
13、朴沈现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,High-order momentsThe moments whose order is higher than 2ndThey are usually used to analyze the non-Gaussian random sequences,离摊暑暗拍咨麓狗喝闪内改眉锅宝更恃索酌醉骏氖带炯岸董约倦评拭迁断现代数字信号处理Advanced Dig
14、ital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,1.2 Stationary Random Sequence,Strict-Sense Stationary Random SequenceThe random sequence with time-invariant probability distribution function or PDFThe numerical characteristics(statistics)of strict-
15、sense stationary random sequence are also time-invariant,丁嚣慕候凌痔搓徽赠疹缨裁饿睫挖唤尧邯等镶旨水紧穗博凛读全帐腺仲殿现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Weakly(Wide-Sense)Stationary Random SequenceThe random sequence satisfiesBoth its 1st-order
16、and 2nd-order moments existFor any integer m,For any integer n1,n2 and m,The weakly stationary random sequence is usually called“stationary random sequence”for short or abbreviated as WSS(wide-sense stationary)random sequence.Notice that a strict-sense stationary signal is not always weakly stationa
17、ry one and most weakly stationary signals are not strict-sense stationary.,眠签谋列斗奄诀焙冈擒盾狄蜡垛刹兔扼兽回呼戍明摹廷姥壳靶神魔嗣版尹现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Properties of(Weakly)Stationary Random SequenceMean square and variance ar
18、e irrelevant to timeAutocovariance is time-shift-invariant Autocorrelation is conjugate symmetrical,耐料耗踪烩椎抖扒蜡滑芯巨轨档增喻承溃聘停喷悼湃碳埠震伶恫措禾硅棠现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Autocorrelation matrix is an Hermite matrix.If x(
19、n)is real signal,then Rxx is real symmetrical and nonnegative definite matrix:,吊苹锐份躬荣俱旦栖雁冕菌簇烃玛猴毙进属社义斌辟亡铡脯怪八欺钉挡锻现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,If x(n)and y(n)are stationary random sequences respectively and they a
20、re jointly stationary,thenIf rxy(m)=0 for any integer m,then x(n)and y(n)are mutually orthogonalIf rxy(m)=mxmy,i.e.covxy(m)=0 for any integer m,then x(n)and y(n)are mutually uncorrelated,啸遁玄野篮铅筏奠仇遁证昧降蚤缀详辩耐害娄狸帘氮癌仕酒千篱旗毁敞番现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digit
21、al Signal Processing_ch1 fundamentals,Properties of Real-Valued Stationary Random SequenceIf random sequences x(n)and y(n)are stationary and real-valued,then,庙鄙霓扭开贡墙犯疙匆耘符芥犹悟掷染死仓啤钥拔逊豆去炕宗釜颧酬唯恍现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fund
22、amentals,1.3 Frequency-Domain Description of Stationary Random Sequence,Wiener-Khintchine Theorem The relation between the autocorrelation function and power spectrum density(PSD)of stationary random sequence x(n):if mx=0,thenrxx(0)is the average power of x(n).,验乞境类砖谚释匝异餐骗韧敏骏唾柔普焙瘪奇窃喘坦楔剔妨淬糟定就衙张现代数字信号
23、处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,Properties of the PSD of Real-Valued Stationary Random SequencePSD is even aboutPSD is real and nonnegativeThe Cross-PSD of Real-Valued Stationary Random Sequences x(n)and y(n),茂珐凛漫嚎英拔味臣建
24、篮岂士袋猫缘儒芍蹭失凡畴絮提籍恳彬值橇联畔谋现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,1.4 The Ergodicity of Stationary Random Sequence,Definition Let xs(n)be a sample(realization)of a stationary stochastic sequence x(n),then x(n)is said to be er
25、godic if,肋阑巡睹珊臃烽辫扇衫四锋稳奏辉尼树堪萌循祝予皱表监矛驯盲绵那肥畅现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals现代数字信号处理Advanced Digital Signal Processing_ch1 fundamentals,The Understanding of ErgodicityThe statistical expectation along the time of one realization is same as the statistical expectation across t
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