表7.1.1线性相位FIR滤波器的幅度特性与相位特性一览表 相位响应 N为奇数 N-1)2 H2(a)=∑c(n)sin(n) e(0)=-0 h(n) H(c0) 况 N c(n) 兀 27 N N为偶数 h(n) (O)=∑d(n) 况 4 N d (n) 2
7.1 Linear-phase FIR transfer function Consider first an Fir filter with a symmetric Impulse response: h(n)=h(N-1-n Its transfer function can be written as H(2)=∑h(m)z=∑h(N-1-m)z By making a change of variable m=N-1 n we can write H(z)=>h(m)z-w--m)=2-(->h(m)zm 期一0 (N-1) H(x-)
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function A real-coefficient polynomial H(z) satisfying the above condition is called a mirror-image polynomial (MIP) o In the case of symmetric impulse response the corresponding expression 1s H(z)=-2 (N-1) H which is called an antimirror-image polynomial (AIP)
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function It follows the relation H(2)=+z (N-1) H(2-) that if z=z is a zero o fH(2), So 1s 2=1/Zi Moreover, for an FIR filter with a real impulse response, the zeros of H(z)occur in complex conjugate pairs Hence, a zero at z=zi is associated with a zero at z=z
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function 11 Re
7.1 Linear-phase FIR transfer function