Second Order Goertzel Filter 为便于分析 ◆Goertzel Filter x[n] -1 y(n] cos N H,)-W欢*云1-袋*z -W x[n]=0,n<0 Multiply both numerator and denominator with for causalLTI system (1-e*2-1) 1-W啖z1 (a) a0。可 1-2cos2z+z2X阿 -1]=[-2]=0。 m-2+2c0s24-+xm,n=01N y[0]=x[0] n]=n]-Wn-] 实现零点因式 实现极点因式 每个K需计算N次 y[N]MN]WNMN-1]-XIk],k=0,1,...,N-1 y],y2]…yLW] 每个K只需计算1次Second Order Goertzel Filter ◆Goertzel Filter ( ) ( )( ) 2 1 1 2 1 2 (1 ) 1 1 j k j k N k j N N k e e z H z z e z    − − − − − − − = − [ ] [ ] [ 1] k y W k N N = − y y N N − =Xk, k=0,1,..., -1 N 1 1 2 1 2 1 2cos k N z k W z z N  − − − − = − + ( ) 1 1 1 k k N H z W z = − − − 1 2 1 1 j k e N z  − = − y y [ 0 −1] [ ] = = −2 y n[ ] Multiply both numerator and denominator with [ ] [ ] [ 1] k y W k n n = − y y n N − n N = 0,1,..., [ ] k y n 实现极点因式 实现零点因式 x[n]=0, n<0 y n[ ] 为便于分析 每个K只需计算1次 每个K需计算N次: for causal LTI system y y y N [1], [2] [ ] 11 2 [ ] y n y n x n [ 2] 2cos [ 1] [ ], N y n k =− − + − + ( ) ( ) k z Y z X = y[0]=x[0]