Ex.7.1 Specifications for LTI DT system If input is bandlimited and sampling frequency is high enough to avoid aliasing,then overall system behaves as an LTI continuous-time system H.U)-Hr(j-0 (ea),24kπ/T 当满足：Nyquist采样定 理条件时，DT系统频率 2pπ/T 响应等于整个等效的CT If H(j)is given 系统频率响应 CID H(ej) DIC xa(t) x(n] y(n Ya(t) T LTI discrete-time system Impulse Invariance effective hin]=Th (nT) continuous-time specifications are converted 】to discrete time specifications by:o=2T,fH(e/o)）=lHe/号)，d 长π 等效CT系统频率响应=DT系统频率响应，在所有数字频率范围内 13
Ex. 7.1 Specifications for LTI DT system 13 ◆If input is bandlimited and sampling frequency is high enough to avoid aliasing, continuous-time specifications are converted to discrete time specifications by: = T, then overall system behaves as an LTI continuous-time system ( ) ( ) ( ) , 0, j T c eff H e T H j H j T = = ， effective T = 当满足: Nyquist采样定 理条件时, DT系统频率 响应等于整个等效的CT 系统频率响应 等效CT系统频率响应=DT系统频率响应, 在所有数字频率范围内 LTI discrete-time system If is given H j c ( ) Impulse Invariance [ ] ( ) c h n Th nT = ( ) ( ), eff H H j j T e =
Ex.7.1 Determining Specifications for a Discrete-Time Filter Specifications of the continuous-time filter: ◆1.passband1-0.01<He(J2<l+0.01,for0≤2≤2π(2000) ◆2.stopband(2l<0.001,for2π(3000)≤2 He(j)川 近似地认为H(2)=0,2π/T=2π5000 δp1=0p21+dp 可作为fmax 离散时间系统 hin]=Th (nT) =0.01 1-62 aliasing avoided nearly 近似满足采样定理 Passband i Transition Stopband T=104s 只需变换频率 2.=2m(10000) 6,=0.0016s2。=2t2000) 由变换公式： =T 0 n.2、=2π(3000) π T下 CT系统频率响应→=DT系统频率响应，当低于Nyquist频率时 14
14 Ex. 7.1 Determining Specifications for a Discrete-Time Filter ◆Specifications of the continuous-time filter: ◆1. passband ◆2. stopband 1 2 0.01 P P = = 0.001 S = 2 (2000) = p 2 (3000) = s 2 (10000) =s 1+ P1 1− P2 S aliasing avoided nearly 4 T s 10− = H j T c ( = ) 0, =2 5000 近似满足采样定理 CT系统频率响应→ =DT系统频率响应, 当低于Nyquist频率时 = T 只需变换频率, 由变换公式: 近似地认为 T 1 0.01 1 0. − + H j for eff( ) 01, 0 2 20 ( 00) H j for eff( ) 0.001, 2 3000 ( ) [ ] ( ) c h n Th nT = 可作为 max f 离散时间系统
Ex.7.1 Determining Specifications for a Discrete-Time Filter Solution: H(e) Specifications of the Same tolerance limits: 1+δp1d discrete-time filter in δn=δp20.01 1-0p2 Hleo）Hn9}Hn(U2) 频率响应相等不变 幅频指标不变 Passband Transition Stopband Hw(U2 δ=0.001 I+ 变换截止频率 0p2 0. 6.4π 0、=0.6π Passband Transition Stopband 0=2T=104Ω 2,=2π(2000) 2.=2π(3000) T=104s 0.001 0 n, 2 T
15 Ex. 7.1 Determining Specifications for a Discrete-Time Filter 4 T s 10− = 4 T 10− = = Specifications of the discrete-time filter in P P 1 2 = =0.01 S =0.001 2 (2000) = p 2 (3000) = s 0.4 p = 0.6 s = Solution: Same tolerance limits: H j eff ( ) ( ) j H e 1+ P1 ( ) eff eff ( ) ( ) j H H j H T e j 1− P2 = = S 1+ P1 1− P2 S 0.001 0.01 幅频指标不变 变换截止频率 频率响应相等不变
关于疫情期间修改平时时成绩比例的通知 根据学校要求，适当调整平时成绩的比例。因此 特别强调考勤，作业，雨课堂互动问题答题，以 及在我主讲的“数字信号处理”慕课上完成每章 测验与网上期未考试，慕课上的测验和期末考试 成绩占平时成绩的一半。 数字信号处理山东大学中国大学MOOC(慕课)网址： https://www.icourse163.org/course/SDU-1449344162 16
16 ◆根据学校要求，适当调整平时成绩的比例。因此 特别强调考勤，作业，雨课堂互动问题答题，以 及在我主讲的“数字信号处理”慕课上完成每章 测验与网上期末考试，慕课上的测验和期末考试 成绩占平时成绩的一半。 数字信号处理_山东大学_中国大学MOOC(慕课)网址： https://www.icourse163.org/course/SDU-1449344162 关于疫情期间修改平时成绩比例的通知
Ex.7.1 Determining Specifications for a Discrete-Time Filter Specifications of the continuous-time filter: ◆1.passband1-0.01<He(j2k1+0.01,for0≤2≤2π(2000) ◆2.stopband(2<0.001,for2π(3000)≤2 CT系统频率响应→=DT系统频率响应 只需由变换公式变换频率： 0=T, T=104s Specifications of the discrete-time filter: ◆1.passband1 -0.01<H(eokl+0.01,for0≤os0.4π ◆2.stopband(e)k0.001,for0.6x≤o 17
17 Ex. 7.1 Determining Specifications for a Discrete-Time Filter ◆Specifications of the continuous-time filter: ◆1. passband ◆2. stopband 4 T s 10− = CT系统频率响应→ =DT系统频率响应 只需由变换公式变换频率: = T, 1 0.01 1 0. − + H j for eff( ) 01, 0 2 20 ( 00) H j for eff( ) 0.001, 2 3000 ( ) ◆Specifications of the discrete-time filter: ◆1. passband ◆2. stopband 1 0.01 1 0. ( ) 0 ,1 0 0.4. j H e for − + ( ) 0.001, 0.6 j H e for