线性相位系统传函和频响第一种频率抽样方法：由： (w)=N=9:奇数 jIm[z]N-1k=2N为奇数：N +1N52Re[z]N=8:偶数jIm[z]N2元N-1k2N2NN为偶数：00(k)=k2Re[z]NN-1kk=NV22
线性相位系统传函和频响 N为奇数： N为偶数： 2 N -1 1 Re[z] jIm[z] N=8:偶数 2 N 1 -1 Re[z] jIm[z] N=9:奇数 ( ) ( ) 2 1 1 0 2 2 2 1 1 1 2 2 ,., ,., N N k k N k N N N k k N N p q p ìï ç - ÷ - - = = í ï ç - ÷ + ï - ç ÷ = - î ( ) ( ) 2 1 0 1 2 2 0 2 2 1 1 1 2 2 ,., ,., N N k k N N k k N N N k k N N p q p ìï - - = - = í = ï - - = + - î ( ) N q w w = -ç -1÷ 2 由：
N-1k2当N为奇数时：N +1kN-12NN当N为偶数时：0k=2NN-J频率响应：2kkTwwwNsin Nsin N22NN2H(k)Nkerkewwwk=1Nsinsinsin222NNN为奇数M=(N-1)/2)N为偶数M=N/2-1
当 N为奇数时： 当 N为偶数时： ( ) ( ) ( ) ( ) ,., ,., N j k N N j N k N N H k e k H k N H k e k N p p ç - ÷ - ç - ÷ - ìï - = = í ï + = - î 2 1 2 2 1 2 1 0 2 1 1 2 ( ) ( ) ( ) ( ) ,., ,., N j k N N j N k N N H k e k N H k k N H k e k N p p ç - ÷ - ç - ÷ - ìï = ç - ÷ = í = ï ï = ç ç + ÷ ÷ - î 2 1 2 2 1 2 0 1 2 0 2 1 1 2 ( ) 1 2 0 2 2 2 2 2 2 ( ) sin sin sin | ( )| sin sin sin Nj j N k k H N N H k N N H e e N k k N N N w w w w p w p w w p w p ç - ÷ - ï ç ÷ ê - + ê ê = í + ê + ï - + î ë 1 M k= üï ú ý ï ûþ å N为奇数M = (N-1)/2, N为偶数M = N/2-1
第一种抽样N=7偶对称奇数点18/ H(ei°) /16/H,(eli0) I[H(k) I14121086A2010.20.40.60.81.21.41.61.820
N = 7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 2 4 6 8 10 12 14 16 18 | H(e j ) | | Hd (e j ) | | H(k) | 第一种抽样 偶对称 奇数点
4arg[H(el")]3210-1-2-312100.20.40.60.81.21.41.61.82
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -4 -3 -2 -1 0 1 2 3 4 arg[H(e j )]
h(n)ha(n)05632021515H(K)[Ha(K)10105C06-10(k)Pd(K)056o
- 1 0 1 2 3 4 5 6 7 01234- 1 0 1 2 3 4 5 6 7 05 1 0 1 5 2 0- 1 0 1 2 3 4 5 6 7 - 4 - 2024 - 1 0 1 2 3 4 5 6 7 0246- 1 0 1 2 3 4 5 6 7 05 1 0 1 5 2 0- 1 0 1 2 3 4 5 6 7 - 4 - 2024 hd(n) |Hd(k)| d(k) h(n) |H(k)| (k)