山东大学：《生物医学信号处理 Biomedical Signal Processing》精品课程教学资源（PPT课件讲稿）Chapter 02 Discrete-Time Signals and Systems

Chapter 2 Discrete-Time Signals and Systems Review of Chapter 2 2.1 Discrete-Time Signals: Sequences High and low frequencies in Discrete-time signal 42.2 Discrete-Time Systems Memoryless(memory): Linear; Time-Invariant Causality stability (biBo 2. 3 Linear Time-Invariant(LTI) Systems ◆ LTI Systems: Convolution(y=gm系统适用吗?) 2.4 Properties of LTI Systems Stability and Causality of LTI systems FIR and IIR systems 2/6/2021 Zhongguo Liu_ Biomedical Engineering_Shandong UniV

2 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Chapter 2 Discrete-Time Signals and Systems ◆2.1 Discrete-Time Signals: Sequences ◆High and Low Frequencies in Discrete-time signal ◆2.2 Discrete-Time Systems ◆Memoryless (memory); Linear; Time-Invariant; Causality; Stability(BIBO) ◆2.3 Linear Time-Invariant (LTI) Systems ◆LTI Systems:Convolution( 系统适用吗?) ◆2.4 Properties of LTI Systems ◆Stability and Causality of LTI systems;FIR and IIR systems; Review of Chapter 2 y n g n x n   = [ ] [ ]

Chapter 2 Discrete-Time Signals and Systems Review of Chapter 2 2.5 Linear Constant-Coefficient Difference Equations The output for a given input is not uniquely specified. Auxiliary conditions are required; initial-rest conditions 92.6 Frequency-Domain Representation of Disarete- Time Signals and systems Eigenfunction and Eigenvalue for LTI systems 2.7 Representation of Sequences by Fourier Transforms 12. 8 Symmetry Properties of the Fourier Transform 2.9 Fourier Transform Theorems 2.10 Discrete-Time Random Signals 2/6/2021 Zhongguo Liu_ Biomedical Engineering

3 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Chapter 2 Discrete-Time Signals and Systems ◆2.5 Linear Constant-Coefficient Difference Equations ◆The output for a given input is not uniquely specified. Auxiliary conditions are required; initial-rest conditions ◆2.6 Frequency-Domain Representation of Discrete￾Time Signals and systems ◆ Eigenfunction and Eigenvalue for LTI systems ◆2.7 Representation of Sequences by Fourier Transforms ◆2.8 Symmetry Properties of the Fourier Transform ◆2.9 Fourier Transform Theorems ◆2.10 Discrete-Time Random Signals Review of Chapter 2

多选题1分 设置 Select the correct description about system: 小]=8nm I The system is Linear. B The system is Time-Invariant The system is Memoryless. I The system is Causal. E If h[n] is the Impulse response of the system, and the system is given an input xin, then the system have the output y]=*x小 hIn=glos[n M*礼=810*x=0C LIIUIyyuu uu Biomedical Engineering_ shandong Univ

4 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Select the correct description about system: The system is Linear. The system is Time-Invariant. The system is Memoryless. The system is Causal. A B C D 提交 If is the Impulse response of the system , and the system is given an input , then the system have the output . E y n g n x n   = [ ] [ ]. y n h n x n   =  [ ] [ ]. h n[ ] x n[ ] h n x n g n x n g x n [ ] [ ] [0] [ ] [ ] [0] [ ]  =  =  h n g n [ ] [0] [ ] =  多选题 1分 multiple choice

多选题1分 设置 Select the correct description about the frequency of the signal x[n]=Acos(oon) A O0=oo is the highest frequency BO=2T is the highest frequency. O%=I is the highest frequency D O=I is the lowest frequency I O=2 is the lowest frequency. 0 is the lowest frequenc g o=aI is lower than 0=AT H 丌 is higher than 提交 5 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

5 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Select the correct description about the frequency of the signal . is the highest frequency. is the highest frequency. is the highest frequency. is the lowest frequency. A B C D 提交 0 x n A n [ ] cos( ) =  0 =  0   = 2   0 = E is the lowest frequency. F is the lowest frequency.   0 = 0   = 2 0  = 0 G is lower than . H is higher than . 0 3 4   = 0 7 4   = 0 3 4   = 0 7 4   = 多选题 1分 multiple choice

多选题1分 设置 Select the correct description about a stable LTI system the impulse response is absolutely summable S=∑小] k= B the impulse response is not absolutely summable S=∑k]→O k If the input x[n]≤B.<a,ral Then the output y[n]<B, <o,for alln 提交 6 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

  k S h k  =− =    6 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Select the correct description about a stable LTI system: the impulse response is absolutely summable the impulse response is not absolutely summable If the input A B C 提交    =− = →   k S h k     , , x x n B for all n   , . y Then the output y n B for all n    多选题 1分 multiple choice

多选题1分 设置 Select the correct description about a causal LTI system i the impulse response hln=o, whenn0 国ixn=xln, for ns 0 then y[n]=y2n], for nsn 提交 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

7 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Select the correct description about a causal LTI system: the impulse response the impulse response the impulse response A B C 提交 multiple choice h n n   =  0, 0. when   0 h n n n =  0, . when h n n     0, 0. when D the impulse response E h n n   =  0, 0. when 1 2 0 if for x n x n n n [ ] [ ], , =  1 2 0 then for y n y n n n [ ] [ ], . =  多选题 1分

单选题1分 设置 For a system with the input and output satisfying a linear constant-coefficient difference equation N M Sayl k=>6xIn-m k=0 m=0 If the system is initially at rest, then the system: is lti but noncausal system B)is LtI and causal system may not be Lti D)is definitely not LTI system. 提交 8 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

8 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. For a system with the input and output satisfying a linear constant-coefficient difference equation, If the system is initially at rest, then the system: is LTI but noncausal system; is LTI and causal system; may not be LTI; is definitely not LTI system. A B C D 提交       = = − = − M m m N k ak y n k b x n m 0 0 单选题 1分

单选题1分 设置 For a system with the input and output satisfying a linear constant-coefficient difference equation N M k=>6xIn-m k=0 m=0 if the system is specified to be linear time-invariant and causal, the output for a given input is: A) not uniquely specified; B) uniquely specified. 提交 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

9 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. For a system with the input and output satisfying a linear constant-coefficient difference equation, if the system is specified to be linear, time-invariant, and causal, the output for a given input is: not uniquely specified; uniquely specified. A B 提交       = = − = − M m m N k ak y n k b x n m 0 0 单选题 1分

单选题1分 设置 For a system with the input and output satisfying a linear constant-coefficient difference equation, N M -]=∑bn-m k=0 m=0 if the system is specified to be linear time-invariant and causal, the auxiliary conditions (initial-rest condit0ns初始松弛杀) are needed, they are A ifn]=0, forn<0, then y[n]=0, fo orn< 0 b ifx[n=0, forn<no, theny[n]=0, forn<n 提交 2/6/2021 Zhongguo liu Biomedical Engineering shandong Univ

10 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. For a system with the input and output satisfying a linear constant-coefficient difference equation, if the system is specified to be linear, time-invariant, and causal, the auxiliary conditions (initial-rest conditions,初始松弛条件) are needed, they are: : A B 提交       = = − = − M m m N k ak y n k b x n m 0 0 if x n for n n then y n for n n  =  =  0 0 , , , . 0 0   if x n for n then y n for n  =  =  0 0 0 0 , , , .   单选题 1分

2.0 Introduction Signal: something conveys information represented mathematically as functions of one or more independent variables classified as Continuous-time(analog) signals, discrete-time signals digital signals Signal-processing systems are classified along the same lines as signals Continuous-time(analog) systems discrete-time systems, digital systems 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ

11 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. 2.0 Introduction ◆Signal: something conveys information, represented mathematically as functions of one or more independent variables. Classified as: ◆Continuous-time (analog) signals, discrete-time signals, digital signals ◆Signal-processing systems are classified along the same lines as signals: Continuous-time (analog) systems, discrete-time systems, digital systems