AN EXAMPLEh(n)a(n)1.50.50.50-0.5-0.5-1-1-1.5-1.5-2-2-2.52.5&240426H(w)p(w)-10-152-200.20.20.40.81.2.1.61.8200.40.60.811.21.41.61.800.611.42[H(eiw)|arg[H(ei)]200.20.40.60.81.21.61.8211.40.20.40.60.81.21.41.61.80A2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -2 0 2 4 6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -2 0 2 4 6 0 2 4 6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 2 4 6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -20 -15 -10 -5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -4 -2 0 2 4 h(n) a(n) H(w) |H(e jw)| (w) arg[H(e jw)]
Case 2：h(n)中心偶对称，N 为偶数NH(w)h(n) e -jn +e -io(N-I-n)H(e w)=null, high pass?n=0NN-1N-1N-12-jw-jwjw2222h(n)+e=e2元wAAn=0VN_元2aN12h(n)cos=en22H(w) = -H(2π-w)n=0H(元) = 0定义一个(N/2+ 1)点序列 b(n):NNb(0) = 0, b(n) = 2hΦ(w)nn=222元元Nw0(w)H(ew)=eb(n)cos w|n-n=0(N-1)元H(w)
H(w) w 2 w 2 (w) -(N-1) H(w) = -H(2-w) H() 0 ( ) 1 2 1 0 1 1 1 1 2 2 2 2 0 1 1 2 2 0 1 2 2 2 0 0 ( ) ( ) ( ) ( )cos ( ) , N j j n j N n n N N N N j j n j n n N Nj n H e h n e e e h n e e N e h n n b b w w w w w w w w - - - - - = - - - - - - - - = - ÷ - - ç = = + = + = ç - - ÷ = å å å 1 2 2 0 2 1 2 2 2 1 2 ( ) ( ) ( ) , , ,., ( ) ( )cos N j N j n H N N n h n n H e e b n n w w w w w ç - ÷ - = = ç - ÷ = = å ç - ÷ 144424443 144444444424444444443 定义一个 (N/2 + 1)点序列 b(n)：
AN EXAMPLEh(n)a(n)1.51.50.50.50.5-0.5-1.51.52406n2H(w)p(w)-10-15200.81.21.61.80.20.40.60.81.20.20.40.61.4011.41.61.81[H(ei)arg[H(ei)]471.20.20.20.40.60.81.41.61.80.40.60.81.21.41.61.811
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -20 -15 -10 -5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -4 -2 0 2 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -4 -2 0 2 4 0 2 4 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 2 4 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 h(n) a(n) H(w) |H(e jw)| (w) arg[H(e jw)]