Three kinds of period of sequence T/o=N a)2r/ω=10,10 2T/O=PHON=P 〔b)2r/心=20/3,=20 c)2π∫ω=2.5π,非周期序
16 Three kinds of period of sequence 2 / = N 2 / = P/Q，N = P
2.1.5 Symmetry of sequence x[n]=xl-nl,even sequence xn==xl-nl odd sequence 0 42024 xn]=x[n conjugate-symmetric sequence xn=-xIn conjugate-antisymmetric sequence
17 2.1.5 Symmetry of sequence x[n] = x[−n],even sequence x[n] = −x[−n],odd sequence [ ] [ ] * x n = x −n [ ] [ ] * x n = −x −n Conjugate-symmetric sequence Conjugate-antisymmetric sequence
x n +x xn=xe-n x-n xIn+x-n xn]-xl-n xIn+x xn+x-i xin-x[-n 2 18
18 x [n] x [ n] o = − o − x[n] x [n] x [n] = e + o x [n] x [ n] e = e − 2 [ ] [ ] [ ] x n x n xe n + − = 2 [ ] [ ] [ ] x n x n x n o − − = x[n] x [n] x [n] e o = + [ ] [ ] * x n x n e = e − [ ] [ ] * x n x n o = − o − 2 [ ] [ ] [ ] * x n x n x n e + − = 2 [ ] [ ] [ ] * x n x n x n o − − =
EXAMPLE xn]=(n+irIn n=-5:5]; 36-6 X[0,0,0,0.0,1,2,34,56]} xe=(X+fliplr(x))/2 xo=(x-fliplr(x))/2 303 subplot(3, 1, 1) stem(n, x) b)e]0 5 subplot(3, 1, 2) stem(n xe subplot(3, 1. 3) stem(n,Xo 3b66609999 Real sequences can be (c)xo(n) 0 5 decomposed into two symmetrical sequences 19
19 [ ] ( 1 ) [ ] 6 x n = n + R n n=[ - 5 : 5 ] ; x=[ 0 , 0 , 0 , 0 , 0 , 1 , 2 , 3 , 4 , 5 , 6 ] ; xe=(x+fliplr(x))/ 2 ; xo=(x -fliplr(x))/ 2 ; subplot( 3 , 1 , 1 ) stem(n,x) subplot(3,1,2) stem(n,xe) subplot(3,1,3) stem(n,xo) EXAMPLE Real sequences can be decomposed into two symmetrical sequences
EXAMPLE Complex sequences can be decomposed into two x]=(1+j)R6[] symmetrical sequences n-5:5l zeros(1, 11); x(n>=0&(n<=5)=(1+j) 0p00000 xe=(x+coni(fliplr(x)))/2 Xo=(x-conj(flipIr(x)))/2 subplot(3, 2, 1 ); 5 0 stem(n, real(x) subplot(3, 2. 2) stem(n, imag) subplot(3, 2,3 stem(n, real(xe)) 2 -5 subplot(3, 2, 4) stem(n, image) subplot(3, 2, 5) stem(n, real(xo )) subplot(3, 2, 6 stem(n, imag(xo)) -5 -5
20 [ ] (1 ) [ ] x n j R6 n n = + n=[-5:5]; x=zeros(1,11); x((n>=0)&(n<=5))=(1+j).^[0:5] xe=(x+conj(fliplr(x)))/2; xo=(x-conj(fliplr(x)))/2 subplot(3,2,1); stem(n,real(x)) subplot(3,2,2); stem(n,imag(x)) subplot(3,2,3); stem(n,real(xe)) subplot(3,2,4); stem(n,imag(xe)) subplot(3,2,5); stem(n,real(xo)) subplot(3,2,6); stem(n,imag(xo)) -5 0 5 -4 -2 0 2 -5 0 5 -4 -2 0 2 -5 0 5 -2 0 2 -5 0 5 -2 0 2 -5 0 5 -2 0 2 -5 0 5 -2 -1 0 1 EXAMPLE Complex sequences can be decomposed into two symmetrical sequences