canonical form realization Introduction to Digital Signal Processing--Transfer Functions Y(=H(X()=1-08) W()=1 1-0.82a) W(2)=0.8zw(a)+X(z) Y(z)=(5+2z1)w(z) y(m)=5w(m)+2w(n-1) 1wm)=0.81n-1)+x(n) y(m)=5w(n)）+2(n-1) w(n) x(n) y(n) wo(n)=0.8w1(n)+x(n) y()-5wo()+2w1() w1(n+1)=wo(n) w(n-1)w1 0.8N 上游充通大￥
Introduction to Digital Signal Processing—— Transfer Functions canonical form realization
canonical form realization Introduction to Digital Signal Processing--Transfer Functions x(n) y(n) w1(n) 0.8 y(n)=w1(n)+5x(n) w1(n+1)=2x(n)+0.8y(n) 上浒充通大
Introduction to Digital Signal Processing—— Transfer Functions canonical form realization
Transfer Function Introduction to Digital Signal Processing--Transfer Functions H(z)= b0+b121+b222++b221 1+a2+a2z2+.+QMz-M amo会2w yn=-a1yn-1-a2Yn-2-..-aMYn-M+boXn+bixn-1+b2Xn-2+.+bLXn-L 上游充通大学
Introduction to Digital Signal Processing—— Transfer Functions Transfer Function
Example Introduction to Digital Signal Processing--Transfer Functions Example 6.2.1:Determine the transfer function of the following third-order FIR filter with im- pulse response: h=[1,6,11,6] y(n)=x(n)+6x(n-1)+11x(n-2)+6x(n-3) H(z)-ho+h1z1+h2Z2+h3z3=1+6z1+11z2+6z3 H(z)=(1+z1)(1+5z1+6z-2)=(1+z1)(1+2z1)(1+3z1) H(w)=1+6ejw+11e-2jw+6e-3fm=(1+ejm)(1+2ejo)(1+3ejo) O=zeros z-plane (I 24 exact zero 0 -3 0 0 W3 unit circle 上游充通大￥
Example Introduction to Digital Signal Processing—— Transfer Functions
Sinusoidal response-steady state response Introduction to Digital Signal Processing--Transfer Functions y(m)=∑h(m)x(m-m)=∑h(m)eo,a-m）=eo,"Σh(m)ejo,m m m m y(n)=H(@)ej@om X(o)=2πδ(0-o) Y(o)=H(o)X(o)=H(o)2πδ(o-oo)=2πH(oo)δ(o-o0) ym)=2元-Y(do=2元2aHo,8a-o,emdo Ho）=|H(）eicHH()otjarge 上游充通大￥
Introduction to Digital Signal Processing—— Transfer Functions Sinusoidal response-steady state response