1、Digital Signal Process ingchap ter 2離散時(shí)間信號與系統(tǒng) 認(rèn)識典型信號，熟悉根本詞匯Unit sample sequenee, Unit step sequenee, exponential sequenee, Sinusoidal seque nee Periodic seque nee, Shift ing , Fold ing , additi on , multiplicati on , Lin ear convolution , Stability/stable , Causality/eausal , Differenee equation, im

2、pulse resp onse正弦序列的周期性LTI系統(tǒng)因果、穩(wěn)定的判斷Stable syein: 丫血出血Causalsvsleiir -» <0example: Give n the impulse resp onse h(n) of a LTI system as1h(n) 0.3nu( n 1), 2h(n) 0.3n u( n)3h(n) 2 nu( n 1)4h(n) 2nu(n)it is a ( causal/not causal, stable/not stable )system.卷積和計(jì)算 convolution：定義：Yi( n)兒(n)*X2( n)X

3、!(m)X2(n m)m掌握不進(jìn)位相乘法求兩個(gè)有限長序列的卷積和，以與有限長序列卷積結(jié)果的 長度，并掌握與第五章圓周卷積之間的關(guān)系ch apter 3DTFT根本詞匯：frequency response, steady state response, sampling, aliasing , Nyquist rate, time shifting、 frequency shifting、 conjugation、 folding、 symmetry、 convolution、Parseval ' s TheoremDTFT定義X(ejw) Fx( n)nx( n)ejwnX(ejw)

4、特點(diǎn)：連續(xù)，以2為周期DTFT性質(zhì)：見教材 48頁熟記常用性質(zhì)，并能利用定義與性質(zhì)求一些序列的DTFTexample: Given x(n)11一(n 2) - (n 2) , thenX(ejW) =Xej(w 2)22Given x(n)X(ejW), then x(n 2)H (ejW) (frequency response)與差分方程(differenee equation)之間的互求，利用H(ejw) 求解系統(tǒng)的穩(wěn)態(tài)響應(yīng)(steady state response)參見教材 56頁 example 3.14example: Given h(n) (0.6)nu(n) , H(ejw

5、), the differenee equation isifx(n) 1.2u(n), then the steady state response yss(n) 抽樣定理理解抽樣定理的意義，什么是Nyquist rate/freque ncy?example : Given a signal(1) x(t) cos(200t) sin(600t) ,(2) x(t) Sa(300t),determ ine the Nyquist rate chapter 4 ZT根本詞匯： ROC，unit circle，zeros, poles，zero-pole plot/zero-pole diag

6、ram ，right-sided sequenee, left-sided sequenee, causal sequenee, finite duration sequeneetwo-sided sequenee, partial fraction expansion ，system function，unit circleZT 定義：X(z)x(n )z n ,收斂域 ROC range of eon verge neen熟記典型序列的z變換一和5("一 U o1-rtr 1n 1example: Given x(n) 2 u( n 1),thenX(z)=， ROC is掌握R

7、OC情況，如：1H(z) (1 0.5z1)1(102：j)(1 1.5z1)，ROC 有哪些情況？記住收斂域不能包含極點(diǎn)ZT性質(zhì)(教材84頁)IZTz反變換，掌握局局部式展開法求z反變換，參見教材90頁example4.7H(z)(system funetion)與系統(tǒng)因果穩(wěn)定性判斷系統(tǒng)因果(causal)條件：H(z)的ROC為圓外且包含無窮處 系統(tǒng)穩(wěn)定(stable)的條件：H(z)的ROC包含單位圓因果穩(wěn)定的條件：H(z)所有極點(diǎn)洛在單位圓(unit circle)example:Give n the freque ncy resp onse of a stable LTI syste

8、m as:會(huì)畫H(z)零極點(diǎn)圖H(z)、H(ejw)以與差分方程之間的關(guān)系以與z變換法求解差分方程(參見教材115頁作業(yè)4.19)H(ejw)jw ejwj2w1 e eDetermi ne:(a) The system function H(z)(b) plot zero-pole diagram(c) differenee equation(d) if it is a causal system, determine h(n)(e) if it is a stable system, determine h(n) ch apter 5 DFTDFS了解頻域采樣定理掌握參見教材125頁與ex

9、ample 5.4DFT /IDFT 定義MJX(k) = DFTx(n)二工工5)呼0 二舟一 ¥ -1AM.y(m)二IDFTX(k)二+"X(k)W*T-l掌握Wn、(n)N的含義，會(huì)根據(jù)定義計(jì)算簡單序列的DFTDFT性質(zhì)掌握圓周翻褶、圓周移位、圓周共軛對稱性、圓周卷積等概念 example: Given the N-point DFT of x(n) is X(k), then N-point DFT of x*(n) is ( )圓周卷積與線性卷積之間的關(guān)系兩個(gè)有限長序列的N點(diǎn)圓周卷積=其線性卷積結(jié)果以N為周期進(jìn)展周期延拓, 再取其主值區(qū)間，會(huì)利用兩者關(guān)系進(jìn)展計(jì)算

10、，掌握兩者相等的條件。2 nexample1：X1(n) (n 1)R5( n),x2( n) sin()R6( n)3if x1(n)©x2(n) x1(n)* x?(n) ,then the minimum value of N =為(n 3)煦(n) example2: Give n 5-po int seque nee as the followJI1M -Ii 1TL1ji3A屮*n(1) Compute the lin ear convo luti ony(n)x(n)* x(n) Compute the 5-poi nt circular con volution x(

11、n) 5 x(n)FFT運(yùn)算量N點(diǎn)基-2FFT radix-2算法的運(yùn)算量，復(fù)數(shù)乘法(complex multiplication)次數(shù)： N|ogN，復(fù)數(shù)加法complex addition次數(shù)：N log：，直接計(jì)算N點(diǎn)DFT的 運(yùn)算量與N2成比例，chap ter 6濾波器結(jié)構(gòu)詞匯：IIR filter,Direct form,Cascade form,Parallel form,FIR filter, Direct form, Cascade form, Lin ear-phase form,Freque ncy sampli ng form會(huì)根據(jù)H(z)的形式或差分方程的形式判斷是F

12、IR濾波器還是IIR濾波器IIR濾波器結(jié)構(gòu)掌握直接型 direct form、級聯(lián)型cascade form、并聯(lián)型 parallel formFIR濾波器結(jié)構(gòu)掌握直接型 direct form、級聯(lián)型cascade form、線性相位 結(jié)構(gòu)linear phase form參見教材219頁作業(yè)6.1,6.2，中文教材220頁作業(yè) 124,7chapter 7Lin ear phase，magn itude， amplitude，main lobe， side lobe，win dow掌握線性相位FIR濾波器的條件兩類理解4種類型的線性相位濾波器適用設(shè)計(jì)的濾波器類型 零點(diǎn)位置特點(diǎn)掌握窗函數(shù)設(shè)計(jì)

13、法的原理chapter 8magn itude squared resp on se, Butterworth lowpass, Chebyshev lowpass (TypeI and II), Elliptic lowpass, Impulse inv aria neemapp ing, Bili neartran sformatio n掌握由|H(j )|2求Ha(s)掌握三種模擬原型低通濾波的特點(diǎn)Butterworth lowpass(P305):整個(gè)頻帶上單調(diào)遞減，具有 3dB不變性Chebyshev lowpass (Type I and ll)(P313):l型在通帶有等波紋特性

14、階數(shù)奇偶的區(qū)別，11型阻帶有等波紋特性階數(shù)奇偶的區(qū)別Elliptic lowpass(P323):通帶、阻帶都有等波紋特性階數(shù)奇偶的區(qū)別模擬濾波器到數(shù)字濾波器的轉(zhuǎn)換方法：雙線性變換法Bilinear tran sformati on、沖擊響應(yīng)不變法Impulse inv aria nee mapp ing，掌握兩 種方法w與 的關(guān)系，給定模擬濾波器的系統(tǒng)函數(shù) H(s)，會(huì)利用兩種方法轉(zhuǎn)換成數(shù)字濾波器H(z)Impulse invariance mapping> Bilmtar Irarusiormalk)nH二 mi.2 Ki-* 二乞2 1- T L+z'1 .rTS-'% #example: Given the system function of an analog filter as the follow:Ha(s)6s 22s 3s 10Set T=1s, determine the system funetion of digital f