上海交通大学：《数字信号处理 Digital Signal Processing（B）》教学资源_Handouts_ch3_Discrete-Time Signals and Systems

Digital Signal Processing (B) Instructor:Zhang Jun 上文大兽

Digital Signal Processing (B) Instructor：Zhang Jun

Course Content Discrete-Time Signals and Systems--Digital Signal Processing Discrete-Time Signals and Systems The Z-Transform Frequency Analysis of Signals and Systems Discrete Fourier Transform (and FFT) Implementations of Discrete-Time Systems Digital Filter Design 上游充〔大学

Discrete-Time Signals and Systems —— Digital Signal Processing Course Content Discrete-Time Signals and Systems The Z-Transform Frequency Analysis of Signals and Systems Discrete Fourier Transform (and FFT) Implementations of Discrete-Time Systems Digital Filter Design

Discrete-Time Signals and Systems Discrete-Time Signals and Systems--Digital Signal Processing Discrete-Time Signals Discrete-Time Systems Analysis of Discrete-Time LTI Systems Discrete-Time Systems Described by Difference Equations Implementation of Discrete-Time Systems Correlation of Discrete-Time Signals 上浒充通大粤

Discrete-Time Signals and Systems —— Digital Signal Processing Discrete-Time Signals and Systems  Discrete-Time Signals  Discrete-Time Systems  Analysis of Discrete-Time LTI Systems  Discrete-Time Systems Described by Difference Equations  Implementation of Discrete-Time Systems  Correlation of Discrete-Time Signals

Discrete-Time Signals Discrete-Time Signals and Systems--Digital Signal Processing 32 ms (a) 256 samples 上游充通大￥

Discrete-Time Signals and Systems —— Digital Signal Processing Discrete-Time Signals

Time-Domain Representation Discrete-Time Signals and Systems--Digital Signal Processing Signals represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x(n)with n being an integer in the range-o≤n≤o x(n)defined only for integer values of n and undefined for non-integer values of n Discrete-time signal represented by {x(n)} 上游充通大

Time-Domain Representation  Signals represented as sequences of numbers, called samples  Sample value of a typical signal or sequence denoted as x (n) with n being an integer in the range －∞≤n≤∞  x(n) defined only for integer values of n and undefined for non-integer values of n  Discrete-time signal represented by {x (n)} Discrete-Time Signals and Systems —— Digital Signal Processing

Unit sample sequence Discrete-Time Signals and Systems--Digital Signal Processing 6(n) &70-{a4oo ●●●●● -2-101234… Representation in MATLAB *A:n=[n1:n2];X=zeros(1,n2-n1+1);X(n0-n1+1)=1; *B:n=[n1:n2];X=[(n-n0)==0]; stem(n,x,'ro'); 0.8 a0.6人 -3<n<3 o0.4 n0=0 0.2 09 -3 2 0 2 上游充通大￥

Discrete-Time Signals and Systems —— Digital Signal Processing Unit sample sequence  Representation in MATLAB A: n=[n1:n2]; x = zeros(1,n2-n1+1); x(n0-n1+1)=1; B: n=[n1:n2]; x = [(n-n0)==0]; stem(n,x,’ro’); ,0,0,1,0,0, 0, 0 1, 0 ( )         n n  n -3 -2 -1 0 1 2 3 0 0.2 0.4 0.6 0.8 1 n  (n-n 0 ) -3<n<3 n0=0

Unit step sequence Discrete-Time Signals and Systems--Digital Signal Processing w网60auu- a--收aaa4sa Representation in MATLAB *A:n=[n1:n2];x=zeros(1,n2-n2+1);xn0-n1+1:end)=1; *B:n=[n1:n2];X=[(n-n0)>=0]; stem(n,x,'ro'); 上游充通大

Unit step sequence Discrete-Time Signals and Systems —— Digital Signal Processing ,0,0,1,1,1, 0, 0 1, 0 ( )         n n u n 1 2 1 0 2 0 0 0 , , 0, 1, ( ) n n n n n n n n n n u n n             Representation in MATLAB A: n=[n1:n2]; x=zeros(1,n2-n2+1); x(n0-n1+1:end)=1; B:n=[n1:n2]; x=[(n-n0)>=0]; stem(n,x,’ro’);

Exponential Signal Discrete-Time Signals and Systems--Digital Signal Processing x(n)=a",Vn,a∈R For Example:x(n)=(0.9)”,0≤n≤10 n=[0:10];x=(0.9).n;stem(n,x,'ro） 0.8 0.6 0.4 0.2 0 0 1 2 3 4 567 89 10 x(n)=eorioo)n,Vn exp 上游充通大

Discrete-Time Signals and Systems —— Digital Signal Processing Exponential Signal x n a n a R n ( )  ,  ;  For Example: x(n)  (0.9) , 0  n 10 n n=[0:10]; x=(0.9).^n; stem(n,x,’ro’) 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 x n e n j n    ( ) , ( )  0 exp

Operations on sequence Discrete-Time Signals and Systems--Digital Signal Processing 1.Signal addition Sample-by-sample addition *{x1(n)}+{x2(n)}={x1(n)+x2(n)} Function [y,n]=sigadd(x1,n1,x2,n2) n=min(min(n1),min(n2)):max(max(n1),max(n2)) y1=zeros(1,length(n));y2=y1; y1(find((n>=min(n1))&(n=min(n2))&(n<=max(n2))==1))=x2; Y=y1+y2; 上游充通大学

Operations on sequence Discrete-Time Signals and Systems —— Digital Signal Processing  1. Signal addition Sample-by-sample addition {x1(n)}+{x2(n)}={x1(n)+x2(n)} Function [y,n]=sigadd(x1,n1,x2,n2) n=min(min(n1),min(n2)): max(max(n1),max(n2)); y1=zeros(1,length(n)); y2=y1; y1(find((n>=min(n1)) & (n=min(n2)) & (n<=max(n2))==1))=x2; Y=y1 + y2;

Operations on sequence Discrete-Time Signals and Systems--Digital Signal Processing 2.Signal multiplication Sample-by-sample multiplication Dot multiplication &{x1(n)}.{x2(n)}={x1(n)×2(n)} Function [y,n]=sigmult(x1,n1,x2,n2) n=min(min(n1),min(n2)):max(max(n1),max(n2)); y1=zeros(1,length(n));y2=y1; y1(find((n>=min(n1))&(n=min(n2))&(n<=max(n2))==1))=x2; Y=y1.*y2; 上游充通大

Operations on sequence Discrete-Time Signals and Systems —— Digital Signal Processing  Sample-by-sample multiplication  Dot multiplication  {x1(n)}.{x2(n)}={x1(n) x2(n)} Function [y,n]=sigmult(x1,n1,x2,n2) n=min(min(n1),min(n2)) : max(max(n1),max(n2)); y1=zeros(1,length(n)); y2=y1; y1(find((n>=min(n1)) & (n=min(n2)) & (n<=max(n2))==1))=x2; Y=y1 .* y2; 2. Signal multiplication